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24987686 | 10.1007/s00031-014-9265-x | We give a complete classification of the reductive symmetric pairs (G,H) for
which the homogeneous space $(G \times H)/diag(H)$ is real spherical in the
sense that a minimal parabolic subgroup has an open orbit.
Combining with a criterion established in [T. Kobayashi--T. Oshima, Adv.
Math. 2013], we give a necessary and sufficient condition for a reductive
symmetric pair $(G,H)$ such that the multiplicities for the branching law of
the restriction any admissible smooth representation of $G$ to $H$ have
finiteness/boundedness property.Comment: To appear in Transformation Groups 19 (2014 | Classification of finite-multiplicity symmetric pairs | classification of finite-multiplicity symmetric pairs | reductive homogeneous diag spherical parabolic subgroup orbit. combining criterion kobayashi oshima adv. math. reductive multiplicities branching restriction admissible finiteness boundedness | non_dup | [] |
46605120 | 10.1007/s00031-014-9274-9 | We study families of reductive group actions on A2 parametrized by curves and show that every faithful action of a non-finite reductive group on A3 is linearizable, i.e. G-isomorphic to a representation of G. The difficulties arise for non-connected groups G. We prove a Generic Equivalence Theorem which says that two affine mor- phisms p: S → Y and q: T → Y of varieties with isomorphic (closed) fibers become isomorphic under a dominant ́etale base change φ : U → Y . A special case is the following result. Call a morphism φ: X → Y a fibration with fiber F if φ is flat and all fibers are (reduced and) isomorphic to F. Then an affine fibration with fiber F admits an ́etale dominant morphism μ: U → Y such that the pull-back is a trivial fiber bundle: U ×Y X ≃ U × F . As an application we give short proofs of the following two (known) results: (a) Every affine A1-fibration over a normal variety is locally trivial in the Zariski-topology; (b) Every affine A2-fibration over a smooth curve is locally trivial in the Zariski-topology | Families of Group Actions, Generic Isotriviality, and Linearization | families of group actions, generic isotriviality, and linearization | families reductive parametrized faithful reductive linearizable i.e. isomorphic difficulties arise generic equivalence says affine phisms varieties isomorphic fibers isomorphic ́etale result. call morphism fibration fiber fibers isomorphic affine fibration fiber admits ́etale morphism pull trivial fiber bundle proofs affine fibration locally trivial zariski topology affine fibration locally trivial zariski topology | non_dup | [] |
25011259 | 10.1007/s00031-014-9277-6 | We prove an equivariant implicit function theorem for variational problems
that are invariant under a varying symmetry group (corresponding to a bundle of
Lie groups). Motivated by applications to families of geometric variational
problems lacking regularity, several non-smooth extensions of the result are
discussed. Among such applications is the submanifold problem of deforming the
ambient metric preserving a given variational property of a prescribed family
of submanifolds, e.g., constant mean curvature, up to the action of the
corresponding ambient isometry groups.Comment: LaTeX2e, 26 pages, to appear in Transform. Group | Deforming solutions of geometric variational problems with varying
symmetry groups | deforming solutions of geometric variational problems with varying symmetry groups | equivariant implicit variational bundle motivated families geometric variational lacking regularity extensions discussed. submanifold deforming ambient preserving variational prescribed submanifolds e.g. curvature ambient isometry latex pages transform. | non_dup | [] |
24986380 | 10.1007/s00031-014-9297-2 | Let $G$ be a connected reductive complex algebraic group. Luna assigned to
any spherical homogeneous space $G/H$ a combinatorial object called a
homogeneous spherical datum. By a theorem of Losev, this object uniquely
determines $G/H$ up to $G$-equivariant isomorphism. In this paper, we determine
the homogeneous spherical datum of a $G$-orbit $X_0$ in a spherical embedding
$G/H \hookrightarrow X$. As an application, we obtain a description of the
colored fan associated to the spherical embedding $X_0 \hookrightarrow
\bar{X_0}$.Comment: 14 pages, 1 tabl | Homogeneous spherical data of orbits in spherical embeddings | homogeneous spherical data of orbits in spherical embeddings | reductive algebraic group. luna assigned spherical homogeneous combinatorial homogeneous spherical datum. losev uniquely determines equivariant isomorphism. homogeneous spherical datum orbit spherical embedding hookrightarrow colored spherical embedding hookrightarrow .comment pages tabl | non_dup | [] |
2184954 | 10.1007/s00031-015-9300-6 | Suppose a finite group acts on a scheme $X$ and a finite-dimensional Lie
algebra $\mathfrak{g}$. The associated equivariant map algebra is the Lie
algebra of equivariant regular maps from $X$ to $\mathfrak{g}$. The irreducible
finite-dimensional representations of these algebras were classified in
previous work with P. Senesi, where it was shown that they are all tensor
products of evaluation representations and one-dimensional representations. In
the current paper, we describe the extensions between irreducible
finite-dimensional representations of an equivariant map algebra in the case
that $X$ is an affine scheme of finite type and $\mathfrak{g}$ is reductive.
This allows us to also describe explicitly the blocks of the category of
finite-dimensional representations in terms of spectral characters, whose
definition we extend to this general setting. Applying our results to the case
of generalized current algebras (the case where the group acting is trivial),
we recover known results but with very different proofs. For (twisted) loop
algebras, we recover known results on block decompositions (again with very
different proofs) and new explicit formulas for extensions. Finally,
specializing our results to the case of (twisted) multiloop algebras and
generalized Onsager algebras yields previously unknown results on both
extensions and block decompositions.Comment: 41 pages; v2: minor corrections, formatting changed to match
published versio | Extensions and block decompositions for finite-dimensional
representations of equivariant map algebras | extensions and block decompositions for finite-dimensional representations of equivariant map algebras | acts mathfrak equivariant equivariant mathfrak irreducible representations algebras classified senesi representations representations. extensions irreducible representations equivariant affine mathfrak reductive. explicitly blocks representations characters extend setting. algebras acting trivial recover proofs. twisted algebras recover decompositions proofs formulas extensions. specializing twisted multiloop algebras onsager algebras unknown extensions pages minor formatting changed match versio | non_dup | [] |
5235246 | 10.1007/s00031-015-9311-3 | Given an infinite reductive group G acting on an affine scheme X over C and a
Hilbert function h: Irr G \to N_0, we construct the moduli space M_{\theta}(X)
of \theta-stable (G,h)-constellations on X, which is a generalization of the
invariant Hilbert scheme after Alexeev and Brion and an analogue of the moduli
space of \theta-stable G-constellations for finite groups introduced by Craw
and Ishii. Our construction of a morphism M_{\theta}(X) \to X//G makes this
moduli space a candidate for a resolution of singularities of the quotient
X//G.Comment: 30 pages, published version and erratu | Moduli spaces of (G,h)-constellations | moduli spaces of (g,h)-constellations | infinite reductive acting affine hilbert moduli theta theta constellations generalization hilbert alexeev brion analogue moduli theta constellations craw ishii. morphism theta moduli candidate singularities quotient pages erratu | non_dup | [] |
24956347 | 10.1007/s00031-015-9325-x | We discuss the construction of Sp(2)Sp(1)-structures whose fundamental form
is closed. In particular, we find 10 new examples of 8-dimensional nilmanifolds
that admit an invariant closed 4-form with stabiliser Sp(2)Sp(1). Our
constructions entail the notion of SO(4)-structures on 7-manifolds. We present
a thorough investigation of the intrinsic torsion of such structures, leading
to the construction of explicit Lie group examples with invariant intrinsic
torsion.Comment: 24 pages; v2, added two remarks concerning a potential analogous
construction related to Spin(7) and the existence of a lattice in the
solvable examples. To appear in Transformation Group | Harmonic structures and intrinsic torsion | harmonic structures and intrinsic torsion | closed. nilmanifolds admit stabiliser constructions entail notion manifolds. thorough intrinsic torsion intrinsic pages remarks concerning analogous solvable examples. | non_dup | [] |
78071697 | 10.1007/s00031-015-9328-7 | Actions of semisimple Hopf algebras H over an algebraically closed field of characteristic zero on commutative domains were classified recently by the authors in [18]. The answer turns out to be very simple–if the action is inner faithful, then H has to be a group algebra. The present article contributes to the non-semisimple case, which is much more complicated. Namely, we study actions of finite dimensional (not necessarily semisimple) Hopf algebras on commutative domains, particularly when H is pointed of finite Cartan type.
The work begins by reducing to the case where H acts inner faithfully on a field; such a Hopf algebra is referred to as Galois-theoretical. We present examples of such Hopf algebras, which include the Taft algebras, uq(sl₂), and some Drinfeld twists of other small quantum groups. We also give many examples of finite dimensional Hopf algebras which are not Galois-theoretical. Classification results on finite dimensional pointed Galois-theoretical Hopf algebras of finite Cartan type will be provided in the sequel, Part II, of this study.National Science Foundation (U.S.) (DMS-1000173)National Science Foundation (U.S.) (DMS-1102548)National Science Foundation (U.S.) (DMS-1401207 | Pointed Hopf Actions On Fields, I | pointed hopf actions on fields, i | semisimple hopf algebras algebraically commutative classified answer turns simple–if faithful algebra. contributes semisimple complicated. necessarily semisimple hopf algebras commutative pointed cartan type. begins reducing acts faithfully hopf referred galois theoretical. hopf algebras taft algebras drinfeld twists groups. hopf algebras galois theoretical. pointed galois hopf algebras cartan sequel study.national foundation u.s. foundation u.s. foundation u.s. | non_dup | [] |
84305482 | 10.1007/s00031-015-9339-4 | This is the accepted manuscript of the following article: Charles Young, ???Quantum loop algebras and l-root operators???, Transformation Groups, Vol. 20(4): 1195-1226, September 2015. The final published version is available at: https://link.springer.com/article/10.1007%2Fs00031-015-9339-4 ?? Springer Science+Business Media New York (2015)Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data (g,q,P), we define an algebra A whose raising/lowering operators are constructed to act with definite l-weight (unlike those of Uq(Lg) itself). It is shown that there is a homomorphism Uq(Lg) -> A such that every representation V in C_P is the pull-back of a representation of A | Quantum loop algebras and l-root operators | quantum loop algebras and l-root operators | charles algebras vol. september springer transcendental. representations poles weights belong specified raising lowering definite unlike homomorphism pull | non_dup | [] |
25025704 | 10.1007/s00031-015-9345-6 | We study Sp(2n,R)-invariant functionals on the spaces of smooth vectors in
Speh representations of GL(2n,R).
For even n we give expressions for such invariant functionals using an
explicit realization of the space of smooth vectors in the Speh
representations. Furthermore, we show that the functional we construct is, up
to a constant, the unique functional on the Speh representation which is
invariant under the Siegel parabolic subgroup of Sp(2n,R). For odd n we show
that the Speh representations do not admit an invariant functional with respect
to the subgroup U(n) of Sp(2n,R) consisting of unitary matrices.
Our construction, combined with the argument in [GOSS12], gives a purely
local and explicit construction of Klyachko models for all unitary
representations of GL(2n,R).Comment: 14 pages. v4: minor corrections in Theorem 2.2, Lemma 2.9 and section | Invariant Functionals on the Speh representation | invariant functionals on the speh representation | functionals speh representations expressions functionals realization speh representations. speh siegel parabolic subgroup speh representations admit subgroup consisting unitary matrices. argument goss purely klyachko unitary representations .comment pages. minor | non_dup | [] |
25033451 | 10.1007/s00031-015-9346-5 | Let $\rho : G \rightarrow \operatorname{O}(V)$ be a real finite dimensional
orthogonal representation of a compact Lie group, let $\sigma =
(\sigma_1,\ldots,\sigma_n) : V \to \mathbb R^n$, where
$\sigma_1,\ldots,\sigma_n$ form a minimal system of homogeneous generators of
the $G$-invariant polynomials on $V$, and set $d = \max_i \operatorname{deg}
\sigma_i$. We prove that for each $C^{d-1,1}$-curve $c$ in $\sigma(V) \subseteq
\mathbb R^n$ there exits a locally Lipschitz lift over $\sigma$, i.e., a
locally Lipschitz curve $\overline c$ in $V$ so that $c = \sigma \circ
\overline c$, and we obtain explicit bounds for the Lipschitz constant of
$\overline c$ in terms of $c$. Moreover, we show that each $C^d$-curve in
$\sigma(V)$ admits a $C^1$-lift. For finite groups $G$ we deduce a
multivariable version and some further results.Comment: 25 pages; section on orbit spaces as differentiable spaces added,
some typos corrected; accepted for publication in Transformation Group | Lifting differentiable curves from orbit spaces | lifting differentiable curves from orbit spaces | rightarrow operatorname orthogonal sigma sigma ldots sigma mathbb sigma ldots sigma homogeneous generators polynomials operatorname sigma sigma subseteq mathbb exits locally lipschitz lift sigma i.e. locally lipschitz overline sigma circ overline bounds lipschitz overline sigma admits lift. deduce multivariable pages orbit differentiable typos corrected publication | non_dup | [] |
42484243 | 10.1007/s00031-015-9353-6 | The final publication is available at Springer via http://dx.doi.org/10.1007/s00031-015-9353-6For any finite-dimensional Lie algebra we introduce the notion of Jordan–Kronecker invariants, study their properties, and discuss examples. These invariants naturally appear in the framework of the bi-Hamiltonian approach to integrable systems on Lie algebras and are closely related to Mischenko–Fomenko’s argument shift method. We also state a generalised argument shift conjecture and prove it for many series of Lie algebras | Jordan-Kronecker invariants of finite-dimensional Lie algebras | jordan-kronecker invariants of finite-dimensional lie algebras | publication springer notion jordan–kronecker invariants examples. invariants naturally integrable algebras closely mischenko–fomenko’s argument method. generalised argument conjecture algebras | non_dup | [] |
52640529 | 10.1007/s00031-015-9355-4 | 23 pagesInternational audienceIn this paper, we study sheets of symmetric Lie algebras through their Slodowy slices. In particular, we introduce a notion of slice induction of nilpotent orbits which coincides with the parabolic induction in the Lie algebra case. We also study in more details the sheets of the non-trivial symmetric Lie algebra of type G2. We characterize their singular loci and provide a nice desingularization lying in so7.In this new version, computations of section 4 are pared down. Important modifications of the exposition of Section 3 on slice induction | Sheets of symmetric Lie algebras and slice induction | sheets of symmetric lie algebras and slice induction | pagesinternational audiencein sheets algebras slodowy slices. notion slice nilpotent orbits coincides parabolic case. sheets trivial characterize singular loci nice desingularization lying computations pared down. modifications exposition slice | non_dup | [] |
25053969 | 10.1007/s00031-016-9370-0 | Consider a Hamiltonian circle action on a closed $8$-dimensional symplectic
manifold $M$ with exactly five fixed points, which is the smallest possible
fixed set. In their paper, L. Godinho and S. Sabatini show that if $M$
satisfies an extra "positivity condition" then the isotropy weights at the
fixed points of $M$ agree with those of some linear action on $\mathbb{CP}^4$.
Therefore, the (equivariant) cohomology rings and the (equivariant) Chern
classes of $M$ and $\mathbb{CP}^4$ agree; in particular, $H^*(M;\mathbb{Z})
\simeq \mathbb{Z}[y]/y^5$ and $c(TM) = (1+y)^5$. In this paper, we prove that
this positivity condition always holds for these manifolds. This completes the
proof of the "symplectic Petrie conjecture" for Hamiltonian circle actions on
on 8-dimensional closed symplectic manifolds with minimal fixed sets.Comment: To appear in Transformation Group | Hamiltonian circle actions on eight dimensional manifolds with minimal
fixed sets | hamiltonian circle actions on eight dimensional manifolds with minimal fixed sets | circle symplectic manifold smallest set. godinho sabatini satisfies extra positivity isotropy weights agree mathbb equivariant cohomology rings equivariant chern mathbb agree mathbb simeq mathbb positivity manifolds. completes symplectic petrie conjecture circle symplectic manifolds | non_dup | [] |
29541042 | 10.1007/s00031-016-9372-y | We compute the Newton--Okounkov bodies of line bundles on the complete flag
variety of GL_n for a geometric valuation coming from a flag of translated
Schubert subvarieties. The Schubert subvarieties correspond to the terminal
subwords in the decomposition (s_1)(s_2s_1)(s_3s_2s_1)(...)(s_{n-1}...s_1) of
the longest element in the Weyl group. The resulting Newton--Okounkov bodies
coincide with the Feigin--Fourier--Littelmann--Vinberg polytopes in type A.Comment: 16 pages, 2 figures, final version, typos corrected, details added, a
new proof (Example 2.9, Remark 2.10) outline | Newton-Okounkov polytopes of flag varieties | newton-okounkov polytopes of flag varieties | newton okounkov bodies bundles flag geometric valuation coming flag translated schubert subvarieties. schubert subvarieties subwords decomposition ...s longest weyl group. newton okounkov bodies coincide feigin fourier littelmann vinberg polytopes pages typos corrected remark outline | non_dup | [] |
74707516 | 10.1007/s00031-016-9377-6 | The main focus of this paper is Bott-Borel-Weil (BBW) theory for basic classical Lie superalgebras. We take a purely algebraic self-contained approach to the problem. A new element in this study is twisting functors, which we use in particular to prove that the top of the cohomology groups of BBW theory for generic weights is described by the recently introduced star action. We also study the algebra of regular functions, related to BBW theory. Then we introduce a weaker form of genericness, relative to the Borel subalgebra and show that the virtual BGG reciprocity of Gruson and Serganova becomes an actual reciprocity in the relatively generic region. We also obtain a complete solution of BBW theory for (m|2), D(2, 1; alpha), F(4) and G(3) with distinguished Borel subalgebra. Furthermore, we derive information about the category of finite-dimensional (m|2)-modules, such as BGG-type resolutions and Kostant homology of Kac modules and the structure of projective modules | Bott-Borel-Weil theory and Bernstein-Gel'Fand-Gel'Fand reciprocity for the Lie superalgebras | bott-borel-weil theory and bernstein-gel'fand-gel'fand reciprocity for the lie superalgebras | bott borel weil superalgebras. purely algebraic problem. twisting functors cohomology generic weights action. theory. weaker genericness borel subalgebra virtual reciprocity gruson serganova reciprocity generic region. alpha distinguished borel subalgebra. derive modules resolutions kostant homology modules projective modules | non_dup | [] |
24974361 | 10.1007/s00031-016-9381-x | In [Wyser-Yong '13] we introduced polynomial representatives of cohomology
classes of orbit closures in the flag variety, for the symmetric pair
$(GL_{p+q}, GL_p \times GL_q)$. We present analogous results for the remaining
symmetric pairs of the form $(GL_n,K)$, i.e., $(GL_n,O_n)$ and
$(GL_{2n},Sp_{2n})$. We establish the well-definedness of certain
representatives from [Wyser '13]. It is also shown that the representatives
have the combinatorial properties of nonnegativity and stability. Moreover, we
give some extensions to equivariant $K$-theory.Comment: 22 pages, 3 figures, 5 tables. Results from V1 have been extended
significantl | Polynomials for symmetric orbit closures in the flag variety | polynomials for symmetric orbit closures in the flag variety | wyser yong representatives cohomology orbit closures flag analogous i.e. establish definedness representatives wyser representatives combinatorial nonnegativity stability. extensions equivariant pages tables. significantl | non_dup | [] |
73391198 | 10.1007/s00031-016-9383-8 | Let $G$ be a simple complex algebraic group, $P$ a parabolic subgroup of $G$
and $N$ the unipotent radical of $P.$ The so-called equivariant
compactification of $N$ by $G/P$ is given by an action of $N$ on $G/P$ with a
dense open orbit isomorphic to $N$. In this article, we investigate how many
such equivariant compactifications there exist. Our result says that there is a
unique equivariant compactification of $N$ by $G/P$, up to isomorphism, except
$\P^n$.Comment: 20 pages, to appear in Transformation Group | Equivariant compactifications of a nilpotent group by $G/P$ | equivariant compactifications of a nilpotent group by $g/p$ | algebraic parabolic subgroup unipotent radical equivariant compactification dense orbit isomorphic equivariant compactifications exist. says equivariant compactification isomorphism .comment pages | non_dup | [] |
29520214 | 10.1007/s00031-016-9387-4 | We associate a root system to a finite set in a free abelian group and prove
that its irreducible subsystem is of type A, B or D. We apply this general
result to a torus manifold, where a torus manifold is a $2n$-dimensional
connected closed smooth manifold with a smooth effective action of an
$n$-dimensional compact torus having a fixed point, and show that if the torus
action extends to a smooth action of a connected compact Lie group $G$, then a
simple factor of the Lie algebra of $G$ is of type A, B or D. This gives an
alternative proof to Wiemeler's theorem. We also discuss a similar problem for
a torus manifold with an invariant stably complex structure. In this case only
type A appears.Comment: 21 pages, v2: deleted Lemma 3.11, added Remark 4.7, references
update | Root systems and symmetries of torus manifolds | root systems and symmetries of torus manifolds | associate abelian irreducible subsystem torus manifold torus manifold manifold torus torus extends wiemeler theorem. torus manifold stably structure. pages deleted remark update | non_dup | [] |
25045697 | 10.1007/s00031-016-9391-8 | Let $B$ be a Borel subgroup of a semisimple algebraic group $G$, and let
$\mathfrak a$ be an abelian ideal of $\mathfrak b=Lie(B)$. The ideal $\mathfrak
a$ is determined by certain subset $\Delta_{\mathfrak a}$ of positive roots,
and using $\Delta_{\mathfrak a}$ we give an explicit classification of the
$B$-orbits in $\mathfrak a$ and $\mathfrak a^*$. Our description visibly
demonstrates that there are finitely many $B$-orbits in both cases. We also
describe the Pyasetskii correspondence between the $B$-orbits in $\mathfrak a$
and $\mathfrak a^*$ and the invariant algebras $\Bbbk[\mathfrak a]^U$ and
$\Bbbk[\mathfrak a^*]^U$, where $U=(B,B)$. As an application, the number of
$B$-orbits in the abelian nilradicals is computed. We also discuss related
results of A.Melnikov and others for classical groups and state a general
conjecture on the closure and dimension of the $B$-orbits in the abelian
nilradicals, which exploits a relationship between between $B$-orbits and
involutions in the Weyl group.Comment: 24 page | On the orbits of a Borel subgroup in abelian ideals | on the orbits of a borel subgroup in abelian ideals | borel subgroup semisimple algebraic mathfrak abelian ideal mathfrak ideal mathfrak delta mathfrak roots delta mathfrak orbits mathfrak mathfrak visibly demonstrates finitely orbits cases. pyasetskii correspondence orbits mathfrak mathfrak algebras bbbk mathfrak bbbk mathfrak orbits abelian nilradicals computed. a.melnikov conjecture closure orbits abelian nilradicals exploits orbits involutions weyl | non_dup | [] |
25051428 | 10.1007/s00031-016-9394-5 | We consider the set of forms of a toric variety over an arbitrary field:
those varieties which become isomorphic to a toric variety after base field
extension. In contrast to most previous work, we also consider arbitrary
isomorphisms rather than just those that respect a torus action. We define an
injective map from the set of forms of a toric variety to a non-abelian second
cohomology set, which generalizes the usual Brauer class of a Severi-Brauer
variety. Additionally, we define a map from the set of forms of a toric variety
to the set of forms of a separable algebra along similar lines to a
construction of A. Merkurjev and I. Panin. This generalizes both a result of
M.~Blunk for del Pezzo surfaces of degree 6, and the standard bijection between
Severi-Brauer varieties and central simple algebrasComment: 41 pages; numerous revisions: introduction more accessible, results
now weaker for singular varieties in positive characteristi | Twisted forms of toric varieties | twisted forms of toric varieties | toric varieties isomorphic toric extension. isomorphisms torus action. injective toric abelian cohomology generalizes usual brauer severi brauer variety. additionally toric separable merkurjev panin. generalizes blunk pezzo bijection severi brauer varieties algebrascomment pages numerous revisions accessible weaker singular varieties characteristi | non_dup | [] |
29554951 | 10.1007/s00031-016-9406-5 | Let $G$ be the product $GL_r(C) \times (C^\times)^n$. We show that the
$G$-equivariant Chow class of a $G$ orbit closure in the space of $r$-by-$n$
matrices is determined by a matroid. To do this, we split the natural
surjective map from the $G$ equvariant Chow ring of the space of matrices to
the torus equivariant Chow ring of the Grassmannian. The splitting takes the
class of a Schubert variety to the corresponding factorial Schur polynomial,
and also has the property that the class of a subvariety of the Grassmannian is
mapped to the class of the closure of those matrices whose row span is in the
variety.Comment: 11 pages. Theorem 3.5 here proves a version of the main result of
arXiv:1306.1810v5, the proof of which contained an erro | Equivariant Chow classes of matrix orbit closures | equivariant chow classes of matrix orbit closures | equivariant chow orbit closure matroid. split surjective equvariant chow torus equivariant chow grassmannian. splitting schubert factorial schur subvariety grassmannian mapped closure span pages. proves erro | non_dup | [] |
29523684 | 10.1007/s00031-016-9409-2 | We show that canonical bases in $\dot{U}(\mathfrak{sl}_n)$ and the Schur
algebra are compatible; in fact we extend this result to $p$-canonical bases.
This follows immediately from a fullness result from a functor categorifying
this map. In order to prove this result, we also explain the connections
between categorifications of the Schur algebra which arise from parity sheaves
on partial flag varieties, singular Soergel bimodules and Khovanov and Lauda's
"flag category," which are of some independent interest.Comment: 12 pages. v2: correcting typo | Comparison of canonical bases for Schur and universal enveloping
algebras | comparison of canonical bases for schur and universal enveloping algebras | canonical bases mathfrak schur compatible extend canonical bases. immediately fullness functor categorifying map. connections categorifications schur arise parity sheaves flag varieties singular soergel bimodules khovanov lauda flag pages. correcting typo | non_dup | [] |
73387442 | 10.1007/s00031-017-9415-z | Geometric structures modeled on rational homogeneous manifolds are studied to
characterize rational homogeneous manifolds and to prove their deformation
rigidity. To generalize these characterizations and deformation rigidity
results to quasihomogeneous varieties, we first study horospherical varieties
and geometric structures modeled on horospherical varieties. Using Cartan
geometry, we prove that a geometric structure modeled on a smooth projective
horospherical variety of Picard number one is locally equivalent to the
standard geometric structure when the geometric structure is defined on a Fano
manifold of Picard number one.Comment: 32 page | Geometric structures modeled on smooth projective horospherical
varieties of Picard number one | geometric structures modeled on smooth projective horospherical varieties of picard number one | geometric modeled rational homogeneous manifolds characterize rational homogeneous manifolds deformation rigidity. generalize characterizations deformation rigidity quasihomogeneous varieties horospherical varieties geometric modeled horospherical varieties. cartan geometric modeled projective horospherical picard locally geometric geometric fano manifold picard | non_dup | [] |
42650716 | 10.1007/s00031-017-9421-1 | We establish the equality of the specialization $E_{w\lambda}(x;q,0)$ of the
nonsymmetric Macdonald polynomial $E_{w\lambda}(x;q,t)$ at $t=0$ with the
graded character $\mathop{\rm gch} U_{w}^{+}(\lambda)$ of a certain
Demazure-type submodule $U_{w}^{+}(\lambda)$ of a tensor product of
"single-column" Kirillov--Reshetikhin modules for an untwisted affine Lie
algebra, where $\lambda$ is a dominant integral weight and $w$ is a (finite)
Weyl group element, this generalizes our previous result, that is, the equality
between the specialization $P_{\lambda}(x;q,0)$ of the symmetric Macdonald
polynomial $P_{\lambda}(x;q,t)$ at $t=0$ and the graded character of a tensor
product of single-column Kirillov--Reshetikhin modules. We also give two
combinatorial formulas for the mentioned specialization of a nonsymmetric
Macdonald polynomial: one in terms of quantum Lakshmibai-Seshadri paths and the
other in terms of the quantum alcove model.Comment: updated reference | A uniform model for Kirillov-Reshetikhin crystals III: Nonsymmetric
Macdonald polynomials at $t=0$ and Demazure characters | a uniform model for kirillov-reshetikhin crystals iii: nonsymmetric macdonald polynomials at $t=0$ and demazure characters | establish equality specialization lambda nonsymmetric macdonald lambda graded character mathop lambda demazure submodule lambda kirillov reshetikhin modules untwisted affine lambda weyl generalizes equality specialization lambda macdonald lambda graded character kirillov reshetikhin modules. combinatorial formulas specialization nonsymmetric macdonald lakshmibai seshadri paths alcove updated | non_dup | [] |
25032679 | 10.1007/s00031-017-9443-8 | We give a combinatorial description of all affine spherical varieties with
prescribed weight monoid $\Gamma$. As an application, we obtain a
characterization of the irreducible components of Alexeev and Brion's moduli
scheme $\mathrm M_\Gamma$ for such varieties. Moreover, we find several
sufficient conditions for $\mathrm M_\Gamma$ to be irreducible and exhibit
several examples where $\mathrm M_\Gamma$ is reducible. Finally, we provide
examples of non-reduced $\mathrm M_\Gamma$.Comment: v4: 26 pages, final versio | On the irreducible components of moduli schemes for affine spherical
varieties | on the irreducible components of moduli schemes for affine spherical varieties | combinatorial affine spherical varieties prescribed monoid gamma irreducible alexeev brion moduli mathrm gamma varieties. mathrm gamma irreducible exhibit mathrm gamma reducible. mathrm gamma .comment pages versio | non_dup | [] |
42742390 | 10.1007/s00031-017-9444-7 | We consider simple modules for a Hecke algebra with a parameter of quantum
characteristic $e$. Equivalently, we consider simple modules $D^{\lambda}$,
labelled by $e$-restricted partitions $\lambda$ of $n$, for a cyclotomic KLR
algebra $R_n^{\Lambda_0}$ over a field of characteristic $p\ge 0$, with mild
restrictions on $p$. If all parts of $\lambda$ are at most $2$, we identify a
set $\mathsf{DStd}_{e,p}(\lambda)$ of standard $\lambda$-tableaux, which is
defined combinatorially and naturally labels a basis of $D^{\lambda}$. In
particular, we prove that the $q$-character of $D^{\lambda}$ can be described
in terms of $\mathsf{DStd}_{e,p}(\lambda)$. We show that a certain natural
approach to constructing a basis of an arbitrary $D^{\lambda}$ does not work in
general, giving a counterexample to a conjecture of Mathas.Comment: Final version, to appear in Transform. Group | On bases of some simple modules of symmetric groups and Hecke algebras | on bases of some simple modules of symmetric groups and hecke algebras | modules hecke equivalently modules lambda labelled restricted partitions lambda cyclotomic lambda mild restrictions lambda mathsf dstd lambda lambda tableaux combinatorially naturally labels lambda character lambda mathsf dstd lambda constructing lambda giving counterexample conjecture transform. | non_dup | [] |
42639790 | 10.1007/s00031-017-9456-3 | We show the natural embedding of weight lattices from a diagram folding is a
virtualization map for the Littelmann path model, which recovers a result of
Kashiwara. As an application, we give a type independent proof that certain
Kirillov--Reshetikhin crystals respect diagram foldings, which is a known
result on a special case of a conjecture given by Okado, Schilling, and
Shimozono.Comment: 14 pages, 1 figure; corrected statement of Theorem 4.2 in v3; minor
corrections from referee report in v | Virtualization map for the Littelmann path model | virtualization map for the littelmann path model | embedding lattices folding virtualization littelmann recovers kashiwara. kirillov reshetikhin crystals foldings conjecture okado schilling pages corrected statement minor referee | non_dup | [] |
73960260 | 10.1007/s00031-017-9469-y | Let $\mathcal{D}$ be the Drinfeld double of the bosonization ${\mathfrak
B}(V)\#\Bbbk G$ of a finite-dimensional Nichols algebra ${\mathfrak B}(V)$ over
a finite group $G$. It is known that the simple $\mathcal{D}$-modules are
parametrized by the simple modules over $\mathcal{D}(G)$, the Drinfeld double
of $G$. This parametrization can be obtained by considering the head
$\mathsf{L}(\lambda)$ of the Verma module $\mathsf{M}(\lambda)$ for every
simple $\mathcal{D}(G)$-module $\lambda$. In the present work, we show that the
projective $\mathcal{D}$-modules are filtered by Verma modules and the BGG
Reciprocity
$[\mathsf{P}(\mu):\mathsf{M}(\lambda)]=[\mathsf{M}(\lambda):\mathsf{L}(\mu)]$
holds for the projective cover $\mathsf{P}(\mu)$ of $\mathsf{L}(\mu)$. We use
graded characters to proof the BGG Reciprocity and obtain a graded version of
it. Also, we show that a Verma module is simple if and only if it is
projective. We also describe the tensor product between projective modules.Comment: 17 pages. v2: We add information about the tensor product between
projective modules [Theorem 4.10]. We show that $\mathcal{D}$ is graded
symmetric [Lemma 3.1] and hence a shift of grading is not needed in the
graded version of the BGG Reciprocity [Corollary 3.6]. Minor changes in
Section | On projective modules over finite quantum groups | on projective modules over finite quantum groups | mathcal drinfeld bosonization mathfrak bbbk nichols mathfrak mathcal modules parametrized modules mathcal drinfeld parametrization mathsf lambda verma module mathsf lambda mathcal module lambda projective mathcal modules filtered verma modules reciprocity mathsf mathsf lambda mathsf lambda mathsf projective cover mathsf mathsf graded characters reciprocity graded verma module projective. projective pages. projective modules mathcal graded grading graded reciprocity corollary minor | non_dup | [] |
163103176 | 10.1007/s00031-018-9479-4 | The best known method to give a lower bound for the Noether number of a given finite group is to use the fact that it is greater than or equal to the Noether number of any of the subgroups or factor groups. The results of the present paper show in particular that these inequalities are strict for proper subgroups or factor groups. This is established by studying the algebra of coinvariants of a representation induced from a representation of a subgroup. © 2018 Springer Science+Business Media, LLC, part of Springer Natur | LOWER BOUNDS ON THE NOETHER NUMBER | lower bounds on the noether number | noether noether subgroups groups. inequalities strict proper subgroups groups. studying coinvariants subgroup. springer springer natur | non_dup | [] |
84094425 | 10.1007/s00031-018-9486-5 | In this short note, we prove that a bi-invariant Riemannian metric on
$\mathrm{Sp}(n)$ is uniquely determined by the spectrum of its Laplace-Beltrami
operator within the class of left-invariant metrics on $\mathrm{Sp}(n)$. In
other words, on any of these compact simple Lie groups, every left-invariant
metric which is not right-invariant cannot be isospectral to a bi-invariant
metric. The proof is elementary and uses a very strong spectral obstruction
proved by Gordon, Schueth, and Sutton.Comment: The proof of Lemma 3.1 was modifie | Spectral uniqueness of bi-invariant metrics on symplectic groups | spectral uniqueness of bi-invariant metrics on symplectic groups | riemannian mathrm uniquely laplace beltrami metrics mathrm isospectral metric. elementary obstruction proved gordon schueth modifie | non_dup | [] |
19715126 | 10.1007/s00032-002-0008-4 | A line congruence is an irreducible subvariety of dimension n−1 in the Grassmannian of lines in Pn. There are two numerical invariants associated to a line congruence: the order, which is the number of lines passing through a general point of Pn, and the class, which is the number of lines of the congruence contained in a general hyperplaneH and meeting a general line inH. The paper reviews the classification of line congruences of order 0 and 1, and then gives some new results online congruences of order 2 in P3, which is a work in progress. The last section states some open questions | Line Congruences of Low Order | line congruences of low order | congruence irreducible subvariety grassmannian invariants congruence passing congruence hyperplaneh meeting inh. reviews congruences congruences progress. | non_dup | [] |
53584460 | 10.1007/s00032-009-0101-z | Phase transitions between two phases are modelled as space regions where a phase-field changes smoothly. The two phases are separated by a thin transition layer, the so-called diffuse interface. All thermodynamic quantities are allowed to vary inside this layer, including the pressure and the mass density. A thermodynamic approach is developed by allowing for the nonlocal character of the continuum. It is based on an extra entropy flux which is proved to be non vanishing inside the transition layer, only. The phase-field is regarded as an internal variable and the kinetic or evolution equation is viewed as a constitutive equation of rate type. Necessary and sufficient restrictions placed by thermodynamics are derived for the constitutive equations and, furthermore, a general form of the evolution equation for the phase-field is obtained within the schemes of both a non-conserved and a conserved phase-field. Based on the thermodynamic restrictions, a phase-field model for the ice-water transition is established which allows for superheating and undercooling. A model ruling the liquid-vapor phase transition is also provided which accounts for both temperature and pressure variations during the evaporation process. The explicit expression of the Gibbs free enthalpy, the Clausius-Clapeyron formula and the customary form of the vapor pressure curve are recovered | Continuum thermodynamics and phase-field models | continuum thermodynamics and phase-field models | modelled smoothly. separated diffuse interface. thermodynamic quantities vary density. thermodynamic allowing nonlocal character continuum. extra proved vanishing only. regarded viewed constitutive type. restrictions placed thermodynamics constitutive schemes conserved conserved field. thermodynamic restrictions superheating undercooling. ruling vapor accounts evaporation process. gibbs enthalpy clausius clapeyron customary vapor recovered | non_dup | [] |
53546676 | 10.1007/s00032-010-0135-2 | The celebrated Brouwer’s Fixed Point Theorem is dated in 1912. Its extension to compact set setting in Banach spaces due to Schauder appeared in 1930. Immediately it raised the question whether the Theorem can be extended to noncompact setting. The works of Kakutani, Klee, Benyamini and Sterfeld, Sternfeld and Lim solved the qualitative part of the problem. Lack of compactness makes the statement of the theorem false. However, there are some quantitative aspects of the question. The two basic are called minimal displacement problem, and optimal retraction problem. The aim of this article is to present the historical back ground and possibly, up to date state of investigations in this field. A list of open problems with comments will be discussed | Why and how much the Brouwer's Fixed Point Theorem fails in noncompact setting? | why and how much the brouwer's fixed point theorem fails in noncompact setting? | celebrated brouwer’s dated banach schauder appeared immediately raised noncompact setting. kakutani klee benyamini sterfeld sternfeld solved qualitative problem. compactness statement false. question. displacement retraction problem. historical possibly investigations field. comments | non_dup | [] |
5240872 | 10.1007/s00032-012-0175-x | We present a survey on several mass transportation problems, in which a given
mass dynamically moves from an initial configuration to a final one. The
approach we consider is the one introduced by Benamou and Brenier in [5], where
a suitable cost functional $F(\rho,v)$, depending on the density $\rho$ and on
the velocity $v$ (which fulfill the continuity equation), has to be minimized.
Acting on the functional $F$ various forms of mass transportation problems can
be modeled, as for instance those presenting congestion effects, occurring in
traffic simulations and in crowd motions, or concentration effects, which give
rise to branched structures.Comment: 16 pages, 14 figures; Milan J. Math., (2012 | Evolution models for mass transportation problems | evolution models for mass transportation problems | transportation dynamically moves one. benamou brenier fulfill continuity minimized. acting transportation modeled presenting congestion occurring traffic crowd motions branched pages milan math. | non_dup | [] |
24943862 | 10.1007/s00032-014-0216-8 | In the continuum, close connections exist between mean curvature flow, the
Allen-Cahn (AC) partial differential equation, and the Merriman-Bence-Osher
(MBO) threshold dynamics scheme. Graph analogues of these processes have
recently seen a rise in popularity as relaxations of NP-complete combinatorial
problems, which demands deeper theoretical underpinnings of the graph
processes. The aim of this paper is to introduce these graph processes in the
light of their continuum counterparts, provide some background, prove the first
results connecting them, illustrate these processes with examples and identify
open questions for future study. We derive a graph curvature from the graph cut
function, the natural graph counterpart of total variation (perimeter). This
derivation and the resulting curvature definition differ from those in earlier
literature, where the continuum mean curvature is simply discretized, and bears
many similarities to the continuum nonlocal curvature or nonlocal means
formulation. This new graph curvature is not only relevant for graph MBO
dynamics, but also appears in the variational formulation of a discrete time
graph mean curvature flow. We prove estimates showing that the dynamics are
trivial for both MBO and AC evolutions if the parameters (the time-step and
diffuse interface scale, respectively) are sufficiently small (a phenomenon
known as "freezing" or "pinning") and also that the dynamics for MBO are
nontrivial if the time step is large enough. These bounds are in terms of graph
quantities such as the spectrum of the graph Laplacian and the graph curvature.
Adapting a Lyapunov functional for the continuum MBO scheme to graphs, we prove
that the graph MBO scheme converges to a stationary state in a finite number of
iterations. Variations on this scheme have recently become popular in the
literature as ways to minimize (continuum) nonlocal total variation.Comment: 76 pages, 7 figures (consisting of 25 subfigures in total) v2 has a
typo in Lemma 5.2, isolated, but important for potential future
use/reference. Corrected in v3. Some ambiguities in Section 3.3 are clarified
in v | Mean curvature, threshold dynamics, and phase field theory on finite
graphs | mean curvature, threshold dynamics, and phase field theory on finite graphs | continuum connections curvature allen cahn merriman bence osher scheme. analogues popularity relaxations combinatorial demands deeper underpinnings processes. continuum counterparts connecting illustrate study. derive curvature counterpart perimeter derivation curvature continuum curvature discretized bears similarities continuum nonlocal curvature nonlocal formulation. curvature variational formulation curvature flow. trivial evolutions diffuse sufficiently phenomenon freezing pinning nontrivial enough. bounds quantities laplacian curvature. adapting lyapunov continuum converges stationary iterations. popular ways minimize continuum nonlocal pages consisting subfigures typo reference. corrected ambiguities clarified | non_dup | [] |
158838644 | 10.1007/s00033-005-0003-z | We study the solutions of a parabolic system of heat equations coupled at the boundary through a nonlinear flux. We characterize in terms of the parameters involved when nonsimultaneous quenching may appear. Moreover, if quenching is non-simultaneous we find the quenching rate, which surprisingly depends on the flux associated to the other component.Fil: Ferreira, Raúl. Universidad Carlos III de Madrid; EspañaFil: de Pablo, Arturo. Universidad Carlos III de Madrid; EspañaFil: Quirós, Fernando. Universidad Autónoma de Madrid; EspañaFil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin | Non-simultaneous quenching in a system of heat equations coupled at the boundary | non-simultaneous quenching in a system of heat equations coupled at the boundary | parabolic flux. characterize nonsimultaneous quenching appear. quenching simultaneous quenching surprisingly component.fil ferreira raúl. universidad carlos madrid españafil pablo arturo. universidad carlos madrid españafil quirós fernando. universidad autónoma madrid españafil rossi julio daniel. universidad buenos aires. facultad ciencias exactas naturales. departamento matemática argentina. consejo nacional investigaciones científicas técnicas argentin | non_dup | [] |
2612848 | 10.1007/s00033-005-0037-2 | Stability of solitary waves in a thin inextensible and unshearable rod of
infinite length is studied. Solitary-wave profile ofthe elastica of such a rod
without torsion has the form of a planar loop and its speed depends on a
tension in the rod. The linear instability of a solitary-wave profile subject
to perturbations escaping from the plane of the loop is established for a
certain range of solitary-wave speeds. It is done using the properties of the
Evans function, an analytic function on the right complex half-plane, that has
zeroes if and only if there exist the unstable modes of the linearization
around a solitary-wave solution. The result follows from comparison of the
behaviour of the Evans function in some neighbourhood of the origin with its
asymptotic at infinity. The explicit computation of the leading coefficient of
the Taylor series of the Evans function near the origin is performed by means
of the symbolic computer language.Comment: 19 pages, 2 figure | Instability of solitary waves on Euler's elastica | instability of solitary waves on euler's elastica | solitary inextensible unshearable infinite studied. solitary ofthe elastica torsion planar tension rod. instability solitary perturbations escaping solitary speeds. evans analytic zeroes unstable linearization solitary solution. evans neighbourhood asymptotic infinity. taylor evans symbolic pages | non_dup | [] |
10883242 | 10.1007/s00033-005-4016-4 | A variety of modelling approaches currently exist to describe and predict the diverse\ud
behaviours of granular materials. One of the more sophisticated theories is hypoplasticity, which is a stress-rate theory of rational continuum mechanics with a constitutive law expressed in a single tensorial equation. In this paper, a particular version of hypoplasticity, due to Wu [2], is employed to describe a class of one-dimensional granular deformations. By combining the constitutive law with the conservation laws of continuum mechanics, a system of four nonlinear partial differential equations is derived for the axial and lateral stress, the velocity and the void ratio. Under certain restrictions, three of the governing equations may be combined to yield\ud
ordinary differential equations, whose solutions can be calculated exactly. Several new analytical results are obtained which are applicable to oedometer testing. In general this approach is not possible, and analytic progress is sought via Lie symmetry analysis. A complete set or "optimal system" of group-invariant solutions is identified using the Olver method, which involves the adjoint representation of the symmetry group on its Lie algebra. Each element in the optimal system is governed by a system of nonlinear ordinary differential equations which in general must be solved numerically. Solutions previously considered in the literature are noted, and their relation to our optimal system identified. Two illustrative examples are examined and the variation of various functions occuring in the physical variables is shown graphically | Symmetry analysis for uniaxial compression of a hypoplastic\ud
granular material | symmetry analysis for uniaxial compression of a hypoplastic\ud granular material | predict diverse behaviours granular materials. sophisticated hypoplasticity rational continuum mechanics constitutive tensorial equation. hypoplasticity granular deformations. combining constitutive conservation laws continuum mechanics axial lateral void ratio. restrictions governing ordinary exactly. applicable oedometer testing. analytic progress sought analysis. olver involves adjoint algebra. governed ordinary solved numerically. identified. illustrative occuring graphically | non_dup | [] |
2595934 | 10.1007/s00033-006-3103-5 | We present a formulation of general nonlinear LC circuits within the
framework of Birkhoffian dynamical systems on manifolds. We develop a
systematic procedure which allows, under rather mild non-degeneracy conditions,
to write the governing equations for the mathematical description of the
dynamics of an LC circuit as a Birkhoffian differential system. In order to
illustrate the advantages of this approach compared to known Lagrangian or
Hamiltonian approaches we discuss a number of specific examples. In particular,
the Birkhoffian approach includes networks which contain closed loops formed by
capacitors, as well as inductor cutsets. We also extend our approach to the
case of networks which contain independent voltage sources as well as
independent current sources. Also, we derive a general balance law for an
associated "energy function".Comment: 26 pages, 2 figures. Z. Angew. Math. Phys. (ZAMP), accepted for
publicatio | Birkhoffian formulation of the dynamics of LC circuits | birkhoffian formulation of the dynamics of lc circuits | formulation circuits birkhoffian manifolds. mild degeneracy governing mathematical circuit birkhoffian system. illustrate advantages lagrangian examples. birkhoffian loops capacitors inductor cutsets. extend sources. derive balance .comment pages figures. angew. math. phys. zamp publicatio | non_dup | [] |
2393159 | 10.1007/s00033-007-6120-0 | We consider the persistence and stability of dark solitons in the
Gross-Pitaevskii (GP) equation with a small decaying potential. We show that
families of black solitons with zero speed originate from extremal points of an
appropriately defined effective potential and persist for sufficiently small
strength of the potential. We prove that families at the maximum points are
generally unstable with exactly one real positive eigenvalue, while families at
the minimum points are generally unstable with exactly two complex-conjugated
eigenvalues with positive real part. This mechanism of destabilization of the
black soliton is confirmed in numerical approximations of eigenvalues of the
linearized GP equation and full numerical simulations of the nonlinear GP
equation with cubic nonlinearity. We illustrate the monotonic instability
associated with the real eigenvalues and the oscillatory instability associated
with the complex eigenvalues and compare the numerical results of evolution of
a dark soliton with the predictions of Newton's particle law for its position.Comment: 39 pages, 10 figure | Dark solitons in external potentials | dark solitons in external potentials | persistence solitons gross pitaevskii decaying potential. families solitons originate extremal appropriately persist sufficiently potential. families unstable eigenvalue families unstable conjugated eigenvalues part. destabilization soliton confirmed approximations eigenvalues linearized cubic nonlinearity. illustrate monotonic instability eigenvalues oscillatory instability eigenvalues soliton newton pages | non_dup | [] |
2082570 | 10.1007/s00033-009-0039-6 | A new method is presented for Fourier decomposition of the Helmholtz Green
Function in cylindrical coordinates, which is equivalent to obtaining the
solution of the Helmholtz equation for a general ring source. The Fourier
coefficients of the Helmholtz Green function are split into their half
advanced+half retarded and half advanced-half retarded components. Closed form
solutions are given for these components in terms of a Horn function and a
Kampe de Feriet function, respectively. The systems of partial differential
equations associated with these two-dimensional hypergeometric functions are
used to construct a fourth-order ordinary differential equation which both
components satisfy. A second fourth-order ordinary differential equation for
the general Fourier coefficent is derived from an integral representation of
the coefficient, and both differential equations are shown to be equivalent.
Series solutions for the various Fourier coefficients are also given, mostly in
terms of Legendre functions and Bessel/Hankel functions. These are derived from
the closed form hypergeometric solutions or an integral representation, or
both. Numerical calculations comparing different methods of calculating the
Fourier coefficients are presented | Exact Fourier expansion in cylindrical coordinates for the
three-dimensional Helmholtz Green function | exact fourier expansion in cylindrical coordinates for the three-dimensional helmholtz green function | fourier decomposition helmholtz cylindrical obtaining helmholtz source. fourier helmholtz split advanced retarded advanced retarded components. horn kampe feriet respectively. hypergeometric fourth ordinary satisfy. fourth ordinary fourier coefficent equivalent. fourier mostly legendre bessel hankel functions. hypergeometric both. calculating fourier | non_dup | [] |
2085343 | 10.1007/s00033-009-0052-9 | We consider the problem of minimising the $k$th eigenvalue, $k \geq 2$, of
the ($p$-)Laplacian with Robin boundary conditions with respect to all domains
in $\mathbb{R}^N$ of given volume $M$. When $k=2$, we prove that the second
eigenvalue of the $p$-Laplacian is minimised by the domain consisting of the
disjoint union of two balls of equal volume, and that this is the unique domain
with this property. For $p=2$ and $k \geq 3$, we prove that in many cases a
minimiser cannot be independent of the value of the constant $\alpha$ in the
boundary condition, or equivalently of the volume $M$. We obtain similar
results for the Laplacian with generalised Wentzell boundary conditions $\Delta
u + \beta \frac{\partial u}{\partial \nu} + \gamma u = 0$.Comment: 16 page | Some remarks on the isoperimetric problem for the higher eigenvalues of
the Robin and Wentzell Laplacians | some remarks on the isoperimetric problem for the higher eigenvalues of the robin and wentzell laplacians | minimising eigenvalue laplacian robin mathbb eigenvalue laplacian minimised consisting disjoint union balls property. minimiser alpha equivalently laplacian generalised wentzell delta beta frac gamma .comment | non_dup | [] |
2105902 | 10.1007/s00033-010-0092-1 | We prove the existence of orbitally stable standing waves with prescribed
$L^2$-norm for the following Schr\"odinger-Poisson type equation \label{intro}
%{%{ll} i\psi_{t}+ \Delta \psi - (|x|^{-1}*|\psi|^{2}) \psi+|\psi|^{p-2}\psi=0
\text{in} \R^{3}, %-\Delta\phi= |\psi|^{2}& \text{in} \R^{3},%. when $p\in
\{8/3\}\cup (3,10/3)$. In the case $3<p<10/3$ we prove the existence and
stability only for sufficiently large $L^2$-norm. In case $p=8/3$ our approach
recovers the result of Sanchez and Soler \cite{SS} %concerning the existence
and stability for sufficiently small charges. The main point is the analysis of
the compactness of minimizing sequences for the related constrained
minimization problem. In a final section a further application to the
Schr\"odinger equation involving the biharmonic operator is given | Stable standing waves for a class of nonlinear Schroedinger-Poisson
equations | stable standing waves for a class of nonlinear schroedinger-poisson equations | orbitally standing prescribed norm schr odinger poisson label intro delta delta sufficiently norm. recovers sanchez soler cite concerning sufficiently charges. compactness minimizing constrained minimization problem. schr odinger involving biharmonic | non_dup | [] |
337562 | 10.1007/s00033-010-0095-y | The official published version can be obtained from the link below.An explicit asymptotic model for transient Love waves is derived from the exact equations of anti-plane elasticity. The perturbation procedure relies upon the slow decay of low-frequency Love waves to approximate the displacement field in the substrate by a power series in the depth coordinate. When appropriate decay conditions are imposed on the series, one obtains a model equation governing the displacement at the interface between the coating and the substrate. Unusually, the model equation contains a term with a pseudo-differential operator. This result is confirmed and interpreted by analysing the exact solution obtained by integral transforms. The performance of the derived model is illustrated by numerical examples.This work is sponsored by the grant from Higher Education of Pakistan and by the Brunel University’s “BRIEF” research award | Explicit asymptotic modelling of transient Love waves propagated along a thin coating | explicit asymptotic modelling of transient love waves propagated along a thin coating | official below.an asymptotic transient love elasticity. perturbation relies slow love approximate displacement coordinate. imposed obtains governing displacement coating substrate. unusually pseudo operator. confirmed interpreted analysing transforms. illustrated examples.this sponsored pakistan brunel university’s “brief” award | non_dup | [] |
2109173 | 10.1007/s00033-011-0156-x | In this paper, we establish existence results for positive solutions to the
Lichnerowicz equation of the following type in closed manifolds -\Delta
u=A(x)u^{-p}-B(x)u^{q},\quad in\quad M, where $p>1, q>0$, and $A(x)>0$,
$B(x)\geq0$ are given smooth functions. Our analysis is based on the global
existence of positive solutions to the following heat equation {ll} u_t-\Delta
u=A(x)u^{-p}-B(x)u^{q},\quad in\quad M\times\mathbb{R}^{+}, u(x,0)=u_0,\quad
in\quad M with the positive smooth initial data $u_0$.Comment: 10 page | Heat flow method to Lichnerowicz type equation on closed manifolds | heat flow method to lichnerowicz type equation on closed manifolds | establish lichnerowicz manifolds delta quad quad functions. delta quad quad mathbb quad quad .comment | non_dup | [] |
24770238 | 10.1007/s00033-011-0157-9 | We consider a 2D system that models the nematic liquid crystal flow through
the Navier--Stokes equations suitably coupled with a
transport-reaction-diffusion equation for the averaged molecular orientations.
This system has been proposed as a reasonable approximation of the well-known
Ericksen--Leslie system. Taking advantage of previous well-posedness results
and proving suitable dissipative estimates, here we show that the system
endowed with periodic boundary conditions is a dissipative dynamical system
with a smooth global attractor of finite fractal dimension | Finite--dimensional global attractor for a system modeling the 2D
nematic liquid crystal flow | finite--dimensional global attractor for a system modeling the 2d nematic liquid crystal flow | nematic navier stokes suitably averaged orientations. reasonable ericksen leslie system. advantage posedness proving dissipative endowed dissipative attractor fractal | non_dup | [] |
48233035 | 10.1007/s00033-011-0163-y | International audienceWe study the eigenpairs of a model Schrödinger operator with a quadratic potential and Neumann boundary conditions on a half-plane. The potential is degenerate in the sense that it reaches its minimum all along a line which makes the angle \theta with the boundary of the half-plane. We show that the first eigenfunctions satisfy localization properties related to the distance to the minimum line of the potential. We investigate the densification of the eigenvalues below the essential spectrum in the limit \theta \to 0 and we prove full asymptotic expansion for these eigenvalues and their associated eigenvectors. We conclude the paper by numerical experiments obtained by a finite element method. The numerical results confirm and enlighten the theoretical approach | Discrete spectrum of a model Schrödinger operator on the half-plane with Neumann conditions | discrete spectrum of a model schrödinger operator on the half-plane with neumann conditions | audiencewe eigenpairs schrödinger quadratic neumann plane. degenerate reaches theta plane. eigenfunctions satisfy localization potential. densification eigenvalues theta asymptotic eigenvalues eigenvectors. method. confirm enlighten | non_dup | [] |
41768149 | 10.1007/s00033-011-0173-9 | In this paper, we extend the earlier work by Quintanilla and Rajagopal (Math Methods Appl Sci 29: 2133–2147,\ud
2006) and establish qualitative new results for a proper generalization of Burgers’ original work that stems form a general\ud
thermodynamic framework. Such fluids have been used to describe the behavior of several geological materials such as\ud
asphalt and the earth’s mantle as well as polymeric fluids. We study questions concerning stability, uniqueness and continuous\ud
dependence on initial data for the solutions of the flows of these fluids. We show that if certain conditions are not\ud
satisfied by the material moduli, the solutions could be unstable. The spatial behavior of the solutions is also analyzed.Peer ReviewedPostprint (published version | Further mathematical results concerning Burgers fluids and their generalizations | further mathematical results concerning burgers fluids and their generalizations | extend quintanilla rajagopal math appl establish qualitative proper generalization burgers’ stems thermodynamic framework. fluids geological asphalt earth’s mantle polymeric fluids. concerning uniqueness flows fluids. satisfied moduli unstable. analyzed.peer reviewedpostprint | non_dup | [] |
24935000 | 10.1007/s00033-011-0185-5 | With this paper we provide an effective method to solve a large class of
problems related to the electromagnetic behavior of thin superconductors. Here
all the problems are reduced to finding the weight functions for the Green
integrals that represent the magnetic field components; these latter must
satisfy the mixed boundary value conditions that naturally arise from the
critical state assumptions. The use of the Erd\'elyi-Kober operators and of the
Hankel transforms (and mostly the employment of their composition properties)
is the keystone to unify the method toward the solution. In fact, the procedure
consists always of the same steps and does not require any peculiar invention.
For this reason the method, here presented in detail for the simplest cases
that can be handled in analytical way (two parts boundary), can be directly
extended to many other more complex geometries (three or more parts), which
usually will require a numerical treatment. In this paper we use the operator
technique to derive the current density and field distributions in perfectly
conducting and superconducting thin discs and tapes subjected to a uniform
magnetic field or carrying a transport current. Although analytical expressions
for the field and current distributions have already been found by other
authors in the past by using several other methods, their derivation is often
cumbersome or missing key details, which makes it difficult for the reader to
fully understand the derivation of the analytical formulas and, more
importantly, to extend the same methods to solve similar new problems. On the
contrary, the characterization of these cases as mixed boundary conditions has
the advantage of referring to an immediate and na\"ive translation of physics
into a consistent mathematical formulation whose possible extension to other
cases is self-evident.Comment: The final publication is available at
http://link.springer.com/article/10.1007/s00033-011-0185- | The critical state in thin superconductors as a mixed boundary value
problem: analysis and solution by means of the Erd\'elyi-Kober operators | the critical state in thin superconductors as a mixed boundary value problem: analysis and solution by means of the erd\'elyi-kober operators | solve electromagnetic superconductors. integrals satisfy naturally arise assumptions. elyi kober hankel transforms mostly employment keystone unify toward solution. peculiar invention. simplest handled geometries treatment. derive perfectly conducting superconducting discs tapes subjected carrying current. expressions derivation cumbersome missing reader derivation formulas importantly extend solve problems. contrary advantage referring immediate translation mathematical formulation publication | non_dup | [] |
52784764 | 10.1007/s00033-012-0232-x | International audienceWe consider a generalized version of Hughes' macroscopic model for crowd motion in the one-dimensional case. It consists in a scalar conservation law accounting for the conservation of the number of pedestrians, coupled with an eikonal equation giving the direction of the flux depending on pedestrian density. As a result of this non-trivial coupling, we have to deal with a conservation law with space-time discontinuous flux, whose discontinuity depends non-locally on the density itself. We propose a definition of entropy weak solution, which allows us to recover a maximum principle. Moreover, we study the structure of the solutions to Riemann-type problems and we construct them explicitly for small times, depending on the choice of the running cost in the eikonal equation. In particular, aiming at the optimization of the evacuation time, we propose a strategy that is optimal in the case of high densities. All results are illustrated by numerical simulations | On entropy weak solutions of Hughes' model for pedestrian motion | on entropy weak solutions of hughes' model for pedestrian motion | audiencewe hughes macroscopic crowd case. conservation accounting conservation pedestrians eikonal giving pedestrian density. trivial deal conservation discontinuous discontinuity locally itself. propose recover principle. riemann explicitly running eikonal equation. aiming evacuation propose densities. illustrated | non_dup | [] |
5232519 | 10.1007/s00033-012-0264-2. | We consider a magnetic Schroedinger operator in a planar infinite strip with
frequently and non-periodically alternating Dirichlet and Robin boundary
conditions. Assuming that the homogenized boundary condition is the Dirichlet
or the Robin one, we establish the uniform resolvent convergence in various
operator norms and we prove the estimates for the rates of convergence. It is
shown that these estimates can be improved by using special boundary
correctors. In the case of periodic alternation, pure Laplacian, and the
homogenized Robin boundary condition, we construct two-terms asymptotics for
the first band functions, as well as the complete asymptotics expansion (up to
an exponentially small term) for the bottom of the band spectrum | Waveguide with non-periodically alternating Dirichlet and Robin
conditions: homogenization and asymptotics | waveguide with non-periodically alternating dirichlet and robin conditions: homogenization and asymptotics | schroedinger planar infinite strip frequently periodically alternating dirichlet robin conditions. homogenized dirichlet robin establish resolvent norms convergence. correctors. alternation laplacian homogenized robin asymptotics asymptotics exponentially | non_dup | [] |
78536584 | 10.1007/s00033-012-0279-8 | Agraïments: The third author thanks the FCT (Portugal) for the partial support through Program POCTI/FEDER and PDCT/MAT/56476/2004.By a sequence of rollings without slipping or twisting along segments of an straight line of the plane a spherical ball of unit radius has to be transferred from an initial state to an arbitrary final state taking into account the orientation of the ball. We provide a new proof that with at most 3 moves we can go from a given initial state to an arbitrary final state. The first proof of this result is due to Hammersley [3]. His proof is more algebraic than ours which is more geometric | The rolling ball problem on the plane revisited | the rolling ball problem on the plane revisited | agraïments thanks portugal pocti feder pdct rollings slipping twisting segments straight spherical ball transferred ball. moves state. hammersley algebraic geometric | non_dup | [] |
54037464 | 10.1007/s00033-012-0297-6 | 19 pagesWe consider the general degenerate hyperbolic-parabolic equation: \begin{equation}\label{E}\tag{E} u_t+\div f(u)-\Delta\phi(u)=0 \mbox{ in } Q = (0,T)\times\Omega,\;\;\;\; T>0,\;\;\;\Omega\subset\mathbb R^N ; \end{equation} with initial condition and the zero flux boundary condition. Here $\phi$ is a continuous non decreasing function. Following [B\"{u}rger, Frid and Karlsen, J. Math. Anal. Appl, 2007], we assume that $f$ is compactly supported (this is the case in several applications) and we define an appropriate notion of entropy solution. Using vanishing viscosity approximation, we prove existence of entropy solution for any space dimension $N\geq 1$ under a partial genuine nonlinearity assumption on $f$. Uniqueness is shown for the case $N=1$, using the idea of [Andreianov and Bouhsiss, J. Evol. Equ., 2004], nonlinear semigroup theory and a specific regularity result for one dimension | Entropy formulation of degenerate parabolic equation with zero-flux boundary condition | entropy formulation of degenerate parabolic equation with zero-flux boundary condition | pageswe degenerate hyperbolic parabolic begin label delta mbox omega omega mathbb condition. decreasing function. rger frid karlsen math. anal. appl compactly notion solution. vanishing viscosity genuine nonlinearity uniqueness andreianov bouhsiss evol. equ. semigroup regularity | non_dup | [] |
2256692 | 10.1007/s00033-013-0302-8 | This paper deals with a nonlinear system of partial differential equations
modeling a simplified tumor-induced angiogenesis taking into account only the
interplay between tumor angiogenic factors and endothelial cells. Considered
model assumes a nonlinear flux at the tumor boundary and a nonlinear
chemotactic response. It is proved that the choice of some key parameters
influences the long-time behaviour of the system. More precisely, we show the
convergence of solutions to different semi-trivial stationary states for
different range of parameters.Comment: 17 page | Long-time behavior of an angiogenesis model with flux at the tumor
boundary | long-time behavior of an angiogenesis model with flux at the tumor boundary | deals simplified angiogenesis interplay angiogenic endothelial cells. assumes chemotactic response. proved influences system. precisely trivial stationary | non_dup | [] |
24765290 | 10.1007/s00033-013-0312-6 | In our previous work, we have established the existence of transonic
characteristic discontinuities separating supersonic flows from a static gas in
two-dimensional steady compressible Euler flows under a perturbation with small
total variation of the incoming supersonic flow over a solid right-wedge. It is
a free boundary problem in Eulerian coordinates and, across the free boundary
(characteristic discontinuity), the Euler equations are of elliptic-hyperbolic
composite-mixed type. In this paper, we further prove that such a transonic
characteristic discontinuity solution is unique and $L^1$--stable with respect
to the small perturbation of the incoming supersonic flow in Lagrangian
coordinates.Comment: 18 pages, 1 figur | Well-Posedness of Transonic Characteristic Discontinuities in
Two-Dimensional Steady Compressible Euler Flows | well-posedness of transonic characteristic discontinuities in two-dimensional steady compressible euler flows | transonic discontinuities separating supersonic flows steady compressible euler flows perturbation incoming supersonic wedge. eulerian discontinuity euler elliptic hyperbolic composite type. transonic discontinuity perturbation incoming supersonic lagrangian pages figur | non_dup | [] |
25037325 | 10.1007/s00033-013-0339-8 | This paper is dedicated to provide theta function representations of
algebro-geometric solutions and related crucial quantities for the
two-component Hunter-Saxton (HS2) hierarchy through studying an
algebro-geometric initial value problem. Our main tools include the polynomial
recursive formalism, the hyperelliptic curve with finite number of genus, the
Baker-Akhiezer functions, the meromorphic function, the Dubrovin-type equations
for auxiliary divisors, and the associated trace formulas. With the help of
these tools, the explicit representations of the algebro-geometric solutions
are obtained for the entire HS2 hierarchy.Comment: 46 pages. accepted for publication J Nonl Math Phys, 2014. arXiv
admin note: substantial text overlap with arXiv:1406.6153, arXiv:1207.0574,
arXiv:1205.6062; and with arXiv:nlin/0105021 by other author | Algebro-geometric solutions for the two-component Hunter-Saxton
hierarchy | algebro-geometric solutions for the two-component hunter-saxton hierarchy | dedicated theta representations algebro geometric crucial quantities hunter saxton hierarchy studying algebro geometric problem. recursive formalism hyperelliptic genus baker akhiezer meromorphic dubrovin auxiliary divisors trace formulas. representations algebro geometric pages. publication nonl math admin substantial overlap nlin | non_dup | [] |
80171890 | 10.1007/s00033-013-0356-7 | In the present work, the tensionless contact problem of an Euler–Bernoulli beam of finite length resting on a two-parameter Pasternak-type foundation is investigated. Owing to the tensionless character of the contact, the beam may lift-off the foundation and the point where contact ceases and detachment begins, named contact locus, needs be assessed. In this situation, a one-dimensional free boundary problem is dealt with. An extra condition, in the form of a homogeneous second-order equation in the displacement and its derivatives, is demanded to set the contact locus and it gives the problem its nonlinear feature. Conversely, the loading and the beam length may be such that the beam rests entirely supported on the foundation, which situation is governed by a classical linear boundary value problem. In this work, contact evolution is discussed for a continuously varying loading condition, starting from a symmetric layout and at a given beam length, until overturning is eventually reached. In particular, stability is numerically assessed through the energy criterion, which is shown to stand for the free boundary situation as well. At overturning, a descending pathway in the system energy appears and stability loss is confirmed | On the stability loss for an euler beam resting on a tensionless pasternak foundation | on the stability loss for an euler beam resting on a tensionless pasternak foundation | tensionless euler–bernoulli resting pasternak foundation investigated. owing tensionless character lift foundation ceases detachment begins named locus assessed. dealt with. extra homogeneous displacement derivatives demanded locus feature. conversely loading rests entirely foundation governed problem. continuously loading layout overturning eventually reached. numerically criterion stand well. overturning descending confirmed | non_dup | [] |
70291464 | 10.1007/s00033-014-0440-7 | In this paper we consider nonautonomous differential systems of arbitrary dimension and first find expressions for their inverse Jacobi multipliers and first integrals in some nonautonomous invariant set in terms of the solutions of the differential system. Given an inverse Jacobi multiplier $V$, we find a relation between the Poincar\'{e} translation map $\Pi$ at time $T$ that extends to arbitrary dimensions the fundamental relation for scalar equations, $V(T,\Pi(x))=V(0,x)\Pi'(x)$, found in Trans. Amer. Math. Soc. 362 (2010), 3591-3612. The main result guarantees the existence of continua of $T$-periodic solutions for $T$-periodic systems in the presence of $T$-periodic first integrals and inverse Jacobi multipliers.The authors are partially supported by a MCYT/FEDER grant number MTM2008-00694
and by a CIRIT grant number 2014 SGR 1204 | Inverse Jacobi multipliers and first integrals for nonautonomous differential systems | inverse jacobi multipliers and first integrals for nonautonomous differential systems | nonautonomous expressions jacobi multipliers integrals nonautonomous system. jacobi multiplier poincar translation extends trans. amer. math. soc. guarantees continua integrals jacobi multipliers.the partially mcyt feder cirit | non_dup | [] |
25020887 | 10.1007/s00033-014-0451-4 | We deal with existence and non-existence of non-negative entire solutions
that blow-up at infinity for a quasilinear problem depending on a non-negative
real parameter. Our main objectives in this paper are to provide far more
general conditions for existence and non-existence of solutions. To this end,
we explore an associated $\mu$-parameter convective ground state problem, sub
and super solutions method combined and an approximation arguments to show
existence of solutions. To show the result of non-existence of solutions, we
follow an idea due to Mitidieri-Pohozaev | Existence and non-existence of Blow-up solutions for a non-autonomous
problem with indefinite and gradient terms | existence and non-existence of blow-up solutions for a non-autonomous problem with indefinite and gradient terms | deal blow infinity quasilinear parameter. objectives solutions. explore convective super arguments solutions. mitidieri pohozaev | non_dup | [] |
78536610 | 10.1007/s00033-014-0460-3 | Agraïments: FEDER-UNAB-10-4E-378. The second author is partially supported by a FAPESP–BRAZIL grant 2013/16492–0. The two authors are also supported by a CAPES CSF–PVE grant 88881.030454/ 2013-01.For m = 1, 2, 3, we consider differential systems of the form x0 = F0(t, x) +Xmi=1εiFi(t, x) + εm+1R(t, x, ε), where Fi: R × D → Rn, and R : R × D × (−ε0, ε0) → Rn are Cm+1 functions, and T–periodic in the first variable, being D an open subset of Rn, and ε a small parameter. For such system we assume that the unperturbed system x0 = F0(t, x) has a k–dimensional manifold of periodic solutions with k ≤ n. We weaken the sufficient assumptions for studying the periodic solutions of the perturbed system when (ε) > 0 is sufficiently small | Improving the averaging theory for computing periodic solutions of the differential equations | improving the averaging theory for computing periodic solutions of the differential equations | agraïments feder unab partially fapesp–brazil capes csf–pve .for εifi t–periodic parameter. unperturbed k–dimensional manifold weaken assumptions studying perturbed sufficiently | non_dup | [] |
25051819 | 10.1007/s00033-015-0495-0 | We consider a family of isotropic volumetric-isochoric decoupled strain
energies $$ F\mapsto W_{\rm eH}(F):=\widehat{W}_{\rm
eH}(U):=\left\{\begin{array}{lll} \frac{\mu}{k}\,e^{k\,\|{\rm dev}_n\log
{U}\|^2}+\frac{\kappa}{2\hat{k}}\,e^{\hat{k}\,[{\rm tr}(\log U)]^2}&\text{if}&
{\rm det}\, F>0,\\ +\infty &\text{if} &{\rm det} F\leq 0,
\end{array}\right.\quad $$ based on the Hencky-logarithmic (true, natural)
strain tensor $\log U$, where $\mu>0$ is the infinitesimal shear modulus,
$\kappa=\frac{2\mu+3\lambda}{3}>0$ is the infinitesimal bulk modulus with
$\lambda$ the first Lam\'{e} constant, $k,\hat{k}$ are dimensionless
parameters, $F=\nabla \varphi$ is the gradient of deformation, $U=\sqrt{F^T F}$
is the right stretch tensor and ${\rm dev}_n\log {U} =\log {U}-\frac{1}{n} {\rm
tr}(\log {U})\cdot 1\!\!1$ is the deviatoric part (the projection onto the
traceless tensors) of the strain tensor $\log U$. For small elastic strains the
energies reduce to first order to the classical quadratic Hencky energy $$
F\mapsto W{_{\rm H}}(F):=\widehat{W}_{_{\rm H}}(U):={\mu}\,\|{\rm dev}_n\log
U\|^2+\frac{\kappa}{2}\,[{\rm tr}(\log U)]^2, $$
which is known to be not rank-one convex.
The main result in this paper is that in plane elastostatics the energies of
the family $W_{_{\rm eH}}$ are polyconvex for $k\geq \frac{1}{3}$,
$\widehat{k}\geq \frac{1}{8}$, extending a previous finding on its rank-one
convexity. Our method uses a judicious application of Steigmann's polyconvexity
criteria based on the representation of the energy in terms of the principal
invariants of the stretch tensor $U$. These energies also satisfy suitable
growth and coercivity conditions. We formulate the equilibrium equations and we
prove the existence of minimizers by the direct methods of the calculus of
variations | The exponentiated Hencky-logarithmic strain energy. Part II: Coercivity,
planar polyconvexity and existence of minimizers | the exponentiated hencky-logarithmic strain energy. part ii: coercivity, planar polyconvexity and existence of minimizers | isotropic volumetric isochoric decoupled mapsto widehat begin array frac frac kappa infty array right. quad hencky logarithmic infinitesimal modulus kappa frac lambda infinitesimal modulus lambda dimensionless nabla varphi deformation sqrt stretch frac cdot deviatoric projection traceless tensors elastic quadratic hencky mapsto widehat frac kappa convex. elastostatics polyconvex frac widehat frac extending convexity. judicious steigmann polyconvexity principal invariants stretch satisfy coercivity conditions. formulate minimizers calculus | non_dup | [] |
25052002 | 10.1007/s00033-015-0498-x | In this paper, we study local bifurcations of an indefinite elliptic system
with multiple components: \begin{equation*}
\left\{\begin{array}{ll}
-\Delta u_j + au_j = \mu_ju_j^3+\beta\sum_{k\ne j}u_k^2u_j,
u_j>0\ \ \hbox{in}\ \Omega, u_j=0 \ \ \hbox{on}\ \partial\Omega,\
j=1,\dots,n.
\end{array}
\right. \end{equation*} Here $\Omega\subset{\mathbb{R}}^N$ is a smooth and
bounded domain, $n\ge3$, $a<-\Lambda_1$ where $\Lambda_1$ is the principal
eigenvalue of $(-\Delta, H_0^1(\Omega))$; $\mu_j$ and $\beta$ are real
constants. Using the positive and non-degenerate solution of the scalar
equation $-\Delta\omega-\omega=-\omega^3$, $\omega\in H_0^1(\Omega)$, we
construct a synchronized solution branch $\mathcal{T}_\omega$. Then we find a
sequence of local bifurcations with respect to $\mathcal{T}_\omega$, and we
find global bifurcation branches of partially synchronized solutions.Comment: 16 pages, 2 figure | Bifurcations for a Coupled Schr\"odinger System with Multiple Components | bifurcations for a coupled schr\"odinger system with multiple components | bifurcations indefinite elliptic begin begin array delta beta hbox omega hbox omega dots array right. omega mathbb lambda lambda principal eigenvalue delta omega beta constants. degenerate delta omega omega omega omega omega synchronized branch mathcal omega bifurcations mathcal omega bifurcation branches partially synchronized pages | non_dup | [] |
29525434 | 10.1007/s00033-015-0532-z | This paper deals with the Neumann boundary value problem for the system
$$u_t=\nabla\cdot\left(D(u)\nabla u\right)-\nabla\cdot\left(S(u)\nabla
v\right)+f(u) ,\quad x\in\Omega,\ t>0$$
$$v_t=\Delta v-v+u,\quad x\in\Omega,\ t>0$$
in a smooth bounded domain $\Omega\subset\mathbb{R}^n$ $(n\geq1)$, where the
functions $D(u)$ and $S(u)$ are supposed to be smooth satisfying $D(u)\geq
Mu^{-\alpha}$ and $S(u)\leq Mu^{\beta}$ with $M>0$, $\alpha\in\mathbb{R}$ and
$\beta\in\mathbb{R}$ for all $u\geq1$, and the logistic source $f(u)$ is smooth
fulfilling $f(0)\geq0$ as well as $f(u)\leq a-\mu u^{\gamma}$ with $a\geq0$,
$\mu>0$ and $\gamma\geq1$ for all $u\geq0$. It is shown that if
$\alpha+2\beta<\gamma-1+\frac{2}{n}$, for $1\leq\gamma<2$ and
$\alpha+2\beta<\gamma-1+\frac{4}{n+2}$, for $\gamma\geq2$,
then for sufficiently smooth initial data the problem possesses a unique
global classical solution which is uniformly bounded.Comment: 10 page | Boundedness in a quasilinear fully parabolic Keller-Segel system with
logistic source | boundedness in a quasilinear fully parabolic keller-segel system with logistic source | deals neumann nabla cdot nabla nabla cdot nabla quad omega delta quad omega omega mathbb supposed satisfying alpha beta alpha mathbb beta mathbb logistic fulfilling gamma gamma alpha beta gamma frac gamma alpha beta gamma frac gamma sufficiently possesses uniformly | non_dup | [] |
80909388 | 10.1007/s00033-015-0534-x | In this paper, we study a system of nonlinear stochastic partial differential equations describing the motion of
turbulent non-Newtonian media in the presence of fluctuating magnetic field. The system is basically obtained by a coupling
of the dynamical equations of a non-Newtonian fluids having p-structure and the Maxwell equations. We mainly show the
existence of weak martingale solutions and their exponential decay when time goes to infinity.Austrian Science Foundation through the Lise Meitner Program M1487 and the.National
Research Foundation of South Africa.http://link.springer.com/journal/332016-10-26hb201 | Existence and large time behavior for a stochastic model of modified magnetohydrodynamic equations | existence and large time behavior for a stochastic model of modified magnetohydrodynamic equations | stochastic describing turbulent newtonian fluctuating field. basically newtonian fluids maxwell equations. martingale exponential goes strian foundation lise meitner the.national foundation africa. | non_dup | [] |
25020224 | 10.1007/s00033-015-0582-2 | This paper deals with a semilinear parabolic system with free boundary in one
space dimension. We suppose that unknown functions $u$ and $v$ undergo
nonlinear reactions $u^q$ and $v^p$, and exist initially in a interval $\{0\leq
x\leq s(0)\}$, but expand to the right with spreading front $\{x=s(t)\}$, with
$s(t)$ evolving according to the free boundary condition $s'(t)=-\mu (u_x+\rho
v_x)$, where $p,\, q,\, \mu, \,\rho$ are given positive constants. The main
purpose of this paper is to understand the existence, uniqueness, regularity
and long time behavior of positive solution or maximal positive solution.
Firstly, we prove that this problem has a unique positive solution $(u,v,s)$
defined in the maximal existence interval $[0,T_{\max})$ when $p,\,q\geq 1$,
while it has a unique maximal positive solution $(u,v,s)$ defined in the
maximal existence interval $[0,T_{\max})$ when $p<1$ or $q<1$. Moreover,
$(u,v,s)$ and $T_{\max}$ have property that either (i) $T_{\max}=+\infty$, or
(ii) $T_{\max}<+\infty$ and
$$ \limsup_{T\nearrow
T_{\max}}\|u,\,v\|_{L^{\infty}([0,T]\times[0,s(t)])}=+\infty.$$ Then we study
the regularity of $(u,v)$ and $s$. At last, we discuss the global existence
($T_{\max}=+\infty$), finite time blow-up ($T_{\max}<+\infty$), and long time
behavior of bounded global solution.Comment: 26 page | A semilinear parabolic system with a free boundary | a semilinear parabolic system with a free boundary | deals semilinear parabolic dimension. unknown undergo initially expand spreading front evolving constants. uniqueness regularity maximal solution. firstly maximal maximal maximal infty infty limsup nearrow infty infty. regularity infty blow infty | non_dup | [] |
29504368 | 10.1007/s00033-015-0601-3 | This paper studies the chemotaxis-haptotaxis system \begin{equation}\nonumber
\left\{ \begin{array}{llc} u_t=\Delta u-\chi\nabla\cdot(u\nabla
v)-\xi\nabla\cdot(u\nabla w)+\mu u(1-u-w), &(x,t)\in \Omega\times (0,T),\\
v_t=\Delta v-v+u, &(x,t)\in\Omega\times (0,T),\\ w_t=-vw,&(x,t)\in \Omega\times
(0,T) \end{array} \right.\quad\quad(\star) \end{equation} under Neumann
boundary conditions. Here $\Omega\subset\mathbb{R}^3$ is a bounded domain with
smooth boundary and the parameters $\xi,\chi,\mu>0$. We prove that for
nonnegative and suitably smooth initial data $(u_0,v_0,w_0)$, if $\chi/\mu$ is
sufficiently small, ($\star$) possesses a global classical solution which is
bounded in $\Omega\times(0,\infty)$. We underline that the result fully
parallels the corresponding parabolic-elliptic-ODE system.Comment: correct Lemma 2.5 in version 1 due to an error in the proof, and
reform Sec.3 to be more clear, main results and arguments remain unchange | Boundedness in a three-dimensional chemotaxis-haptotaxis model | boundedness in a three-dimensional chemotaxis-haptotaxis model | chemotaxis haptotaxis begin nonumber begin array delta nabla cdot nabla nabla cdot nabla omega delta omega omega array right. quad quad neumann conditions. omega mathbb nonnegative suitably sufficiently possesses omega infty underline parallels parabolic elliptic reform sec. arguments unchange | non_dup | [] |
29543162 | 10.1007/s00033-016-0616-4 | In this paper, we are concerned with optimal decay rates for higher order
spatial derivatives of classical solutions to the full compressible MHD
equations in three dimensional whole space. If the initial perturbation are
small in $H^3$-norm and bounded in $L^q(q\in \left[1,
\frac{6}{5}\right))$-norm, we apply the Fourier splitting method by
Schonbek[Arch. Rational Mech. Anal. 88 (1985)] to establish optimal decay rates
for the second order spatial derivatives of solutions and the third order
spatial derivatives of magnetic field in $L^2$-norm. These results improve the
work of Pu and Guo [Z. Angew. Math. Phys. 64 (2013) 519-538].Comment: 26 pages. arXiv admin note: substantial text overlap with
arXiv:1505.0042 | Optimal Decay Rates of Classical Solutions for the Full Compressible MHD
Equations | optimal decay rates of classical solutions for the full compressible mhd equations | concerned derivatives compressible space. perturbation norm frac norm fourier splitting schonbek arch. rational mech. anal. establish derivatives derivatives norm. angew. math. phys. .comment pages. admin substantial overlap | non_dup | [] |
80139708 | 10.1007/s00033-016-0628-0 | We consider the amplitude equation for nonlinear surface wave solutions of hyperbolic conservation laws. This is an asymptotic nonlocal, Hamiltonian evolution equation with quadratic nonlinearity. For example, this equation describes the propagation of nonlinear Rayleigh waves, surface waves on current-vortex sheets in incompressible MHD and on the incompressible plasma-vacuum interface. \ud
The local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables was shown in a previous article. In the present paper we prove the continuous dependence in strong norm of solutions on the initial data. This completes the proof of the well-posedness of the problem in the classical sense of Hadamard | Data dependence for the amplitude equation of surface waves | data dependence for the amplitude equation of surface waves | hyperbolic conservation laws. asymptotic nonlocal quadratic nonlinearity. describes propagation rayleigh vortex sheets incompressible incompressible interface. cauchy noncanonical article. norm data. completes posedness hadamard | non_dup | [] |
42643703 | 10.1007/s00033-016-0629-z | A compactness framework is formulated for the incompressible limit of
approximate solutions with weak uniform bounds with respect to the adiabatic
exponent for the steady Euler equations for compressible fluids in any
dimension. One of our main observations is that the compactness can be achieved
by using only natural weak estimates for the mass conservation and the
vorticity. Another observation is that the incompressibility of the limit for
the homentropic Euler flow is directly from the continuity equation, while the
incompresibility of the limit for the full Euler flow is from a combination of
all the Euler equations. As direct applications of the compactness framework,
we establish two incompressible limit theorems for multidimensional steady
Euler flows through infinitely long nozzles, which lead to two new existence
theorems for the corresponding problems for multidimensional steady
incompressible Euler equations.Comment: 17 pages; 2 figures. arXiv admin note: text overlap with
arXiv:1311.398 | Incompressible Limit of Solutions of Multidimensional Steady
Compressible Euler Equations | incompressible limit of solutions of multidimensional steady compressible euler equations | compactness formulated incompressible approximate bounds adiabatic exponent steady euler compressible fluids dimension. compactness conservation vorticity. incompressibility homentropic euler continuity incompresibility euler euler equations. compactness establish incompressible theorems multidimensional steady euler flows infinitely nozzles theorems multidimensional steady incompressible euler pages figures. admin overlap | non_dup | [] |
42685792 | 10.1007/s00033-016-0631-5 | In this article, we prove the existence and multiplicity of positive
solutions for the following fractional elliptic equation with sign-changing
weight functions: \begin{eqnarray*} \left\{\begin{array}{l@{\quad }l}
(-\Delta)^\alpha u= a_\lambda(x)|u|^{q-2}u+b(x)|u|^{2^*_\alpha-1}u &{\rm
in}\,\,\Omega, u=0\,\,&{\rm in}\,\,\R^N\setminus\Omega, \end{array} \right.
\end{eqnarray*} where $0<\alpha<1$, $ \Omega $ is a bounded domain with smooth
boundary in $ \R^N $ with $N>2\alpha$ and $ 2^*_\alpha=2N/(N-2\alpha)$ is the
fractional critical Sobolev exponent. Our multiplicity results are based on
studying the decomposition of the Nehari manifold and the
Ljusternik-Schnirelmann category | Multiple positive solutions for nonlinear critical fractional elliptic
equations involving sign-changing weight functions | multiple positive solutions for nonlinear critical fractional elliptic equations involving sign-changing weight functions | multiplicity fractional elliptic changing begin eqnarray begin array quad delta alpha lambda alpha omega setminus omega array right. eqnarray alpha omega alpha alpha alpha fractional sobolev exponent. multiplicity studying decomposition nehari manifold ljusternik schnirelmann | non_dup | [] |
24983698 | 10.1007/s00033-016-0648-9 | We study the stationary Keller--Segel chemotaxis models with logistic
cellular growth over a one-dimensional region subject to the Neumann boundary
condition. We show that nonconstant solutions emerge in the sense of Turing's
instability as the chemotaxis rate $\chi$ surpasses a threshold number. By
taking the chemotaxis rate as the bifurcation parameter, we carry out
bifurcation analysis on the system to obtain the explicit formulas of
bifurcation values and small amplitude nonconstant positive solutions. Moreover
we show that solutions stay strictly positive in the continuum of each branch.
The stabilities of these steady state solutions are well studied when the
creation and degradation rate of the chemical is assumed to be a linear
function. Finally we investigate the asymptotic behaviors of the monotone
steady states. We construct solutions with interesting patterns such as a
boundary spike when the chemotaxis rate is large enough and/or the cell
motility is small.Comment: Zeitschrift f\"ur Angewandte Mathematik und Physik, 201 | Qualitative analysis of stationary Keller-Segel chemotaxis models with
logistic growth | qualitative analysis of stationary keller-segel chemotaxis models with logistic growth | stationary keller segel chemotaxis logistic neumann condition. nonconstant emerge turing instability chemotaxis surpasses number. chemotaxis bifurcation carry bifurcation formulas bifurcation nonconstant solutions. stay strictly continuum branch. stabilities steady creation degradation function. asymptotic behaviors monotone steady states. spike chemotaxis motility zeitschrift angewandte mathematik physik | non_dup | [] |
29526806 | 10.1007/s00033-016-0652-0 | We are concerned with the acoustic scattering problem, at a frequency
$\kappa$, by many small obstacles of arbitrary shapes with impedance boundary
condition. These scatterers are assumed to be included in a bounded domain
$\Omega$ in $\mathbb{R}^3$ which is embedded in an acoustic background
characterized by an eventually locally varying index of refraction. The
collection of the scatterers $D_m, \; m=1,...,M$ is modeled by four parameters:
their number $M$, their maximum radius $a$, their minimum distance $d$ and the
surface impedances $\lambda_m, \; m=1,...,M$. We consider the parameters $M, d$
and $\lambda_m$'s having the following scaling properties: $M:=M(a)=O(a^{-s})$,
$d:=d(a)\approx a^t$ and $\lambda_m:=\lambda_m(a)=\lambda_{m,0}a^{-\beta}$, as
$a \rightarrow 0$, with non negative constants $s, t$ and $\beta$ and complex
numbers $\lambda_{m, 0}$'s with eventually negative imaginary parts.
We derive the asymptotic expansion of the farfields with explicit error
estimate in terms of $a$, as $a\rightarrow 0$. The dominant term is the
Foldy-Lax field corresponding to the scattering by the point-like scatterers
located at the centers $z_m$'s of the scatterers $D_m$'s with $\lambda_m \vert
\partial D_m\vert$ as the related scattering coefficients.Comment: 27 pages, 1figur | Multiscale analysis of the acoustic scattering by many scatterers of
impedance type | multiscale analysis of the acoustic scattering by many scatterers of impedance type | concerned acoustic kappa obstacles shapes impedance condition. scatterers omega mathbb embedded acoustic eventually locally refraction. scatterers modeled impedances lambda lambda approx lambda lambda lambda beta rightarrow beta lambda eventually imaginary parts. derive asymptotic farfields rightarrow foldy scatterers centers scatterers lambda vert vert pages figur | non_dup | [] |
42659287 | 10.1007/s00033-016-0669-4 | We consider a class of elasticity equations in ${\mathbb R}^d$ whose elastic
moduli depend on $n$ separated microscopic scales, are random and expressed as
a linear expansion of a countable sequence of random variables which are
independently and identically uniformly distributed in a compact interval. The
multiscale Hellinger-Reissner problem that allows for computing the stress
directly, and the multiscale mixed problem for nearly incompressible isotropic
materials are considered. The stochastic problems are studied via deterministic
problems that depend on a countable number of real parameters. We study the
multiscale homogenized problems that contain all the macroscopic and
microscopic information, whose solutions are written as generalized polynomial
chaos (gpc) expansions. We approximate these solutions by semidiscrete Galerkin
approximating problems that project into the spaces of functions with only a
finite number of $N$ gpc modes. We deduce bounds and summability properties for
the solutions' gpc expansion coefficients, which imply explicit rates of
convergence in terms of $N$ when the gpc modes used for the Galerkin
approximation are chosen to correspond to the best $N$ terms in the gpc
expansion. For the mixed problem for nearly incompressible materials, the rate
of convergence for the best $N$ term approximation is independent of the Lam\'e
constants' ratio. We establish parametric correctors in terms of the
semidiscrete Galerkin approximations. For two scale problems, an explicit
homogenization rate is deduced. Together with the best $N$ term rate, it
provides an explicit convergence rate for the correctors of the parametric
multiscale problems. For nearly incompressible materials, we obtain a
homogenization rate that is independent of the ratio of the Lam\'e constants,
so that the error for the corrector is also independent of this ratio | Polynomial approximations of a class of stochastic multiscale elasticity
problems | polynomial approximations of a class of stochastic multiscale elasticity problems | elasticity mathbb elastic moduli separated microscopic countable independently identically uniformly interval. multiscale hellinger reissner multiscale nearly incompressible isotropic considered. stochastic deterministic countable parameters. multiscale homogenized macroscopic microscopic chaos expansions. approximate semidiscrete galerkin approximating modes. deduce bounds summability imply galerkin expansion. nearly incompressible ratio. establish parametric correctors semidiscrete galerkin approximations. homogenization deduced. correctors parametric multiscale problems. nearly incompressible homogenization corrector | non_dup | [] |
29520694 | 10.1007/s00033-016-0673-8 | We investigate the long term behavior in terms of finite dimensional global
and exponential attractors, as time goes to infinity, of solutions to a
semilinear reaction-diffusion equation on non-smooth domains subject to
nonlocal Robin boundary conditions, characterized by the presence of fractional
diffusion on the boundary. Our results are of general character and apply to a
large class of irregular domains, including domains whose boundary is Holder
continuous and domains which have fractal-like geometry. In addition to
recovering most of the existing results on existence, regularity, uniqueness,
stability, attractor existence, and dimension, for the well-known
reaction-diffusion equation in smooth domains, the framework we develop also
makes possible a number of new results for all diffusion models in other
non-smooth settings.Comment: 39 pages, 3 figures. arXiv admin note: text overlap with
arXiv:0901.4412 by other author | Long-term behavior of reaction-diffusion equations with nonlocal
boundary conditions on rough domains | long-term behavior of reaction-diffusion equations with nonlocal boundary conditions on rough domains | exponential attractors goes infinity semilinear nonlocal robin fractional boundary. character irregular holder fractal geometry. recovering regularity uniqueness attractor pages figures. admin overlap | non_dup | [] |
78546838 | 10.1007/s00033-016-0682-7 | Agraïments: The first author is supported by CNPq 248501/2013-5. CAPES grant 88881.030454 /2013-01 from the Program CSF-PVEThe usual averaging theory reduces the computation of some periodic solutions of a system of ordinary differential equations, to find the simple zeros of an associated averaged function. When one of these zeros is not simple, i.e. the Jacobian of the averaged function in it is zero, the classical averaging theory does not provide information about the periodic solution associated to a non simple zero. Here we provide sufficient conditions in order that the averaging theory can be applied also to non simple zeros for studying their associated periodic solutions. Additionally we do two applications of this new result for studying the zero--Hopf bifurcation in the Lorenz system and in the Fitzhugh--Nagumo system | New results on averaging theory and applications | new results on averaging theory and applications | agraïments cnpq capes pvethe usual averaging reduces ordinary zeros averaged function. zeros i.e. jacobian averaged averaging zero. averaging zeros studying solutions. additionally studying hopf bifurcation lorenz fitzhugh nagumo | non_dup | [] |
42684885 | 10.1007/s00033-016-0686-3 | Reaction-diffusion equations with a nonlinear source have been widely used to
model various systems, with particular application to biology. Here, we provide
a solution technique for these types of equations in $N$-dimensions. The
nonclassical symmetry method leads to a single relationship between the
nonlinear diffusion coefficient and the nonlinear reaction term; the subsequent
solutions for the Kirchhoff variable are exponential in time (either growth or
decay) and satisfy the linear Helmholtz equation in space. Example solutions
are given in two dimensions for particular parameter sets for both quadratic
and cubic reaction terms.Comment: 18 pages, 6 figure | Exact solutions for logistic reaction-diffusion in biology | exact solutions for logistic reaction-diffusion in biology | widely biology. dimensions. nonclassical kirchhoff exponential satisfy helmholtz space. quadratic cubic pages | non_dup | [] |
84589251 | 10.1007/s00033-016-0690-7 | This research was supported in part by the Australian Research Council (DP140100339) and by the French National Research Agency through the ANR blanche project Kibord [ANR-13-BS01-0004] and the “ANR JC” project Modevol [ANR-13-JS01-0009]. TL was also supported in part by the Hadamard Mathematics Labex, backed by the Fondation Mathématique Jacques Hadamard, through a grant overseen by the French National Research Agency [ANR-11-LABX-0056-LMH]. LD was also supported in part by Université Sorbonne Paris Cité “Investissements d’Avenir”[ANR-11-IDEX-0005].Epigenetic mechanisms are increasingly recognised as integral to the adaptation of species that face environmental changes. In particular, empirical work has provided important insights into the contribution of epigenetic mechanisms to the persistence of clonal species, from which a number of verbal explanations have emerged that are suited to logical testing by proof-of-concept mathematical models. Here, we present a stochastic agent-based model and a related deterministic integrodifferential equation model for the evolution of a phenotype-structured population composed of asexually-reproducing and competing organisms which are exposed to novel environmental conditions. This setting has relevance to the study of biological systems where colonising asexual populations must survive and rapidly adapt to hostile environments, like pathogenesis, invasion and tumour metastasis. We explore how evolution might proceed when epigenetic variation in gene expression can change the reproductive capacity of individuals within the population in the new environment. Simulations and analyses of our models clarify the conditions under which certain evolutionary paths are possible, and illustrate that whilst epigenetic mechanisms may facilitate adaptation in asexual species faced with environmental change, they can also lead to a type of “epigenetic load” and contribute to extinction. Moreover, our results offer a formal basis for the claim that constant environments favour individuals with low rates of stochastic phenotypic variation. Finally, our model provides a “proof of concept” of the verbal hypothesis that phenotypic stability is a key driver in rescuing the adaptive potential of an asexual lineage, and supports the notion that intense selection pressure can, to an extent, offset the deleterious effects of high phenotypic instability and biased epimutations, and steer an asexual population back from the brink of an evolutionary dead end.PostprintPeer reviewe | Evolutionary dynamics of phenotype-structured populations : from individual-level mechanisms to population-level consequences | evolutionary dynamics of phenotype-structured populations : from individual-level mechanisms to population-level consequences | australian council french agency blanche kibord “anr modevol hadamard mathematics labex backed fondation mathématique jacques hadamard overseen french agency labx université sorbonne paris cité “investissements d’avenir” idex .epigenetic increasingly recognised adaptation changes. insights epigenetic persistence clonal verbal explanations emerged suited logical mathematical models. stochastic agent deterministic integrodifferential phenotype structured composed asexually reproducing competing organisms exposed conditions. relevance colonising asexual survive rapidly adapt hostile environments pathogenesis invasion tumour metastasis. explore proceed epigenetic reproductive environment. clarify evolutionary paths illustrate whilst epigenetic facilitate adaptation asexual faced “epigenetic load” extinction. offer formal claim environments favour stochastic phenotypic variation. “proof concept” verbal phenotypic driver rescuing adaptive asexual lineage supports notion intense offset deleterious phenotypic instability biased epimutations steer asexual brink evolutionary dead end.postprintpeer reviewe | non_dup | [] |
42645999 | 10.1007/s00033-016-0696-1 | The purpose of this paper is to obtain existence and uniqueness results in
weighted Sobolev spaces for transmission problems for the non-linear
Darcy-Forchheimer-Brinkman system and the linear Stokes system in two
complementary Lipschitz domains in ${\mathbb R}^3$, one of them is a bounded
Lipschitz domain $\Omega $ with connected boundary, and another one is the
exterior Lipschitz domain ${\mathbb R}^3\setminus \overline{\Omega }$. We
exploit a layer potential method for the Stokes and Brinkman systems combined
with a fixed point theorem in order to show the desired existence and
uniqueness results, whenever the given data are suitably small in some weighted
Sobolev spaces and boundary Sobolev spaces.Comment: 29 page | Integral potential method for a transmission problem with Lipschitz
interface in ${\mathbb R}^3$ for the Stokes and Darcy-Forchheimer-Brinkman
PDE systems | integral potential method for a transmission problem with lipschitz interface in ${\mathbb r}^3$ for the stokes and darcy-forchheimer-brinkman pde systems | uniqueness weighted sobolev darcy forchheimer brinkman stokes complementary lipschitz mathbb lipschitz omega exterior lipschitz mathbb setminus overline omega exploit stokes brinkman desired uniqueness whenever suitably weighted sobolev sobolev | non_dup | [] |
29563042 | 10.1007/s00033-016-0702-7 | We consider a coexistence of two axisymmetric liquid bridges LB_i and LB_m of
two immiscible liquids i and m which are immersed in a third liquid (or gas) e
and trapped between two smooth solid bodies with axisymmetric surfaces S_1,S_2
and free contact lines. Evolution of liquid bridges allows two different
configurations of LB_i and LB_m with multiple (five or three) interfaces of
non-smooth shape. We formulate a variational problem with volume constraints
and present its governing equations supplemented by boundary conditions. We
find a universal relationship between curvature of the interfaces and discuss
the Young relation at the singular curve where all liquids meet together.Comment: 14 pages, 4 Figure | Multiple Liquid Bridges with Non-Smooth Interfaces | multiple liquid bridges with non-smooth interfaces | coexistence axisymmetric bridges immiscible liquids immersed trapped bodies axisymmetric lines. bridges configurations interfaces shape. formulate variational governing supplemented conditions. universal curvature interfaces singular liquids meet pages | non_dup | [] |
42678221 | 10.1007/s00033-016-0705-4 | In this paper we study the boundary controllability of the Gear-Grimshaw
system posed on a finite domain $(0,L)$, with Neumann boundary conditions:
\begin{equation} \label{abs} \begin{cases} u_t + uu_x+u_{xxx} + a v_{xxx} +
a_1vv_x+a_2 (uv)_x =0, & \text{in} \,\, (0,L)\times (0,T), c v_t +rv_x
+vv_x+abu_{xxx} +v_{xxx}+a_2buu_x+a_1b(uv)_x =0, & \text{in} \,\, (0,L)\times
(0,T), u_{xx}(0,t)=h_0(t),\,\,u_x(L,t)=h_1(t),\,\,u_{xx}(L,t)=h_2(t), &
\text{in} \,\, (0,T),
v_{xx}(0,t)=g_0(t),\,\,v_x(L,t)=g_1(t),\,\,v_{xx}(L,t)=g_2(t), & \text{in} \,\,
(0,T), u(x,0)= u^0(x), \quad v(x,0)= v^0(x), & \text{in} \,\, (0,L).\nonumber
\end{cases} \end{equation} We first prove that the corresponding linearized
system around the origin is exactly controllable in $(L^2(0,L))^2$ when
$h_2(t)=g_2(t)=0$. In this case, the exact controllability property is derived
for any $L>0$ with control functions $h_0, g_0\in H^{-\frac{1}{3}}(0,T)$ and
$h_1, g_1\in L^2(0,T)$. If we change the position of the controls and consider
$h_0(t)=h_2(t)=0$ (resp. $g_0(t)=g_2(t)=0)$ we obtain the result with control
functions $g_0, g_2\in H^{-\frac{1}{3}}(0,T)$ and $h_1, g_1\in L^2(0,T)$ if and
only if the length $L$ of the spatial domain $(0,L)$ belongs to a countable
set. In all cases the regularity of the controls are sharp in time. If only one
control act in the boundary condition, $h_0(t)=g_0(t)=h_2(t)=g_2(t)=0$ and
$g_1(t)=0$ (resp. $h_1(t)=0$), the linearized system is proved to be exactly
controllable for small values of the length $L$ and large time of control $T$.
Finally, the nonlinear system is shown to be locally exactly controllable via
the contraction mapping principle, if the associated linearized systems are
exactly controllable.Comment: 30 Page | Neumann Boundary Controllability of the Gear--Grimshaw System With
Critical Size Restrictions on the Spacial Domain | neumann boundary controllability of the gear--grimshaw system with critical size restrictions on the spacial domain | controllability gear grimshaw posed neumann begin label begin quad nonumber linearized controllable controllability frac resp. frac belongs countable set. regularity sharp time. resp. linearized proved controllable locally controllable contraction linearized | non_dup | [] |
73354070 | 10.1007/s00033-016-0717-0 | This paper mainly investigates the approximation of a global maximizer of the
1-D Monge-Kantorovich mass transfer problem through the approach of nonlinear
differential equations with Dirichlet boundary. Using an approximation
mechanism, the primal maximization problem can be transformed into a sequence
of minimization problems. By applying the canonical duality theory, one is able
to derive a sequence of analytic solutions for the minimization problems. In
the final analysis, the convergence of the sequence to a global maximizer of
the primal Monge-Kantorovich problem will be demonstrated.Comment: 10 pages, 0 figure. arXiv admin note: text overlap with
arXiv:1607.06554, arXiv:1607.0655 | Analytic solutions for the approximated 1-D Kantorovich mass transfer
problems | analytic solutions for the approximated 1-d kantorovich mass transfer problems | investigates maximizer monge kantorovich dirichlet boundary. primal maximization transformed minimization problems. canonical duality derive analytic minimization problems. maximizer primal monge kantorovich pages figure. admin overlap | non_dup | [] |
42688554 | 10.1007/s00033-016-0721-4 | We apply parallel approaches in the study of continuous spectra to adiabatic
stellar models. We seek continuum eigenmodes for the LAWE formulated as both
finite difference and linear differential equations. In particular, we apply
methods of Jacobi matrices and methods of subordinancy theory in these
respective formulations. We find certain pressure-density conditions which
admit positive-measured sets of continuous oscillation spectra under plausible
conditions on density and pressure. We arrive at results of unbounded
oscillations and computational or, perhaps, dynamic instability | Continuum Eigenmodes in Some Linear Stellar Models | continuum eigenmodes in some linear stellar models | adiabatic models. seek continuum eigenmodes lawe formulated equations. jacobi subordinancy respective formulations. admit oscillation plausible pressure. arrive unbounded oscillations perhaps instability | non_dup | [] |
73357747 | 10.1007/s00033-017-0768-x | The response of mechanical systems composed of springs and dashpots to a step
input is of eminent interest in the applications. If the system is formed by
linear elements, then its response is governed by a system of linear ordinary
differential equations, and the mathematical method of choice for the analysis
of the response of such systems is the classical theory of distributions.
However, if the system contains nonlinear elements, then the classical theory
of distributions is of no use, since it is strictly limited to the linear
setting. Consequently, a question arises whether it is even possible or
reasonable to study the response of nonlinear systems to step inputs. The
answer is positive. A mathematical theory that can handle the challenge is the
so-called Colombeau algebra. Building on the abstract result by (Pr\r{u}\v{s}a
& Rajagopal 2016, Int. J. Non-Linear Mech) we show how to use the theory in the
analysis of response of a simple nonlinear mass--spring--dashpot system | Colombeau algebra as a mathematical tool for investigating step load and
step deformation of systems of nonlinear springs and dashpots | colombeau algebra as a mathematical tool for investigating step load and step deformation of systems of nonlinear springs and dashpots | composed springs dashpots eminent applications. governed ordinary mathematical distributions. strictly setting. arises reasonable inputs. answer positive. mathematical handle challenge colombeau algebra. rajagopal int. mech spring dashpot | non_dup | [] |
42674267 | 10.1007/s00033-017-0772-1 | A cross-diffusion system for two compoments with a Laplacian structure is
analyzed on the multi-dimensional torus. This system, which was recently
suggested by P.-L. Lions, is formally derived from a Fokker-Planck equation for
the probability density associated to a multi-dimensional It\={o} process,
assuming that the diffusion coefficients depend on partial averages of the
probability density with exponential weights. A main feature is that the
diffusion matrix of the limiting cross-diffusion system is generally neither
symmetric nor positive definite, but its structure allows for the use of
entropy methods. The global-in-time existence of positive weak solutions is
proved and, under a simplifying assumption, the large-time asymptotics is
investigated | A cross-diffusion system derived from a Fokker-Planck equation with
partial averaging | a cross-diffusion system derived from a fokker-planck equation with partial averaging | compoments laplacian torus. lions formally fokker planck averages exponential weights. limiting neither definite methods. proved simplifying asymptotics | non_dup | [] |
42639730 | 10.1007/s00033-017-0779-7 | It is shown that the gap solution and critical transition temperature are
significantly enhanced by doping in a recently developed BCS formalism for
graphene superconductivity in such a way that positive gap and transition
temperature both occur in arbitrary pairing coupling as far as doping is
present. The analytic construction of the BCS gap and transition temperature
offers highly effective globally convergent iterative methods for the
computation of these quantities. A series of numerical examples are presented
as illustrations consolidating the analytic understanding achieved.Comment: 21 pages, 8 figure | Determination of Gap Solution and Critical Temperature in Doped Graphene
Superconductivity | determination of gap solution and critical temperature in doped graphene superconductivity | doping formalism graphene superconductivity pairing doping present. analytic offers globally convergent iterative quantities. illustrations consolidating analytic pages | non_dup | [] |
42696455 | 10.1007/s00033-017-0780-1 | For any inhomogeneous compactly supported electromagnetic (EM) medium, it is
shown that there exists an infinite set of linearly independent electromagnetic
waves which generate nearly vanishing scattered wave fields. If the
inhomogeneous medium is coated with a layer of properly chosen conducting
medium, then the wave set is generated from the Maxwell-Herglotz approximation
to the interior PEC or PMC eigenfunctions and depends only on the shape of the
inhomogeneous medium. If no such a conducting coating is used, then the wave
set is generated from the Maxwell-Herglotz approximation to the generalised
interior transmission eigenfunctions and depends on both the content and the
shape of the inhomogeneous medium. We characterise the nearly non-scattering
wave sets in both cases with sharp estimates. The results can be used to give a
conceptual design of a novel shadowless lamp. The crucial ingredient is to
properly choose the source of the lamp so that nearly no shadow will be
produced by the surgeons operating under the lamp.Comment: 18 pages, 1 figur | Nearly non-scattering electromagnetic wave set and its application | nearly non-scattering electromagnetic wave set and its application | inhomogeneous compactly electromagnetic infinite linearly electromagnetic nearly vanishing scattered fields. inhomogeneous coated properly conducting maxwell herglotz interior eigenfunctions inhomogeneous medium. conducting coating maxwell herglotz generalised interior eigenfunctions inhomogeneous medium. characterise nearly sharp estimates. conceptual shadowless lamp. crucial ingredient properly lamp nearly shadow surgeons operating pages figur | non_dup | [] |
42748760 | 10.1007/s00033-017-0781-0 | We consider the damped wave equation with Dirichlet boundary conditions on
the unit square. We assume the damping to be a characteristic function of a
strip. We prove the exact $t^{-4/3}$-decay rate for the energy of classical
solutions. This answers a question of Anantharaman and L\'eautaud (2014).Comment: 10 pages. In version 2 we corrected a minor mistake in the
formulation of Theorem 1. A slightly extended and revised version of the
paper will be published in the "Zeitschrift f\"ur angewandte Mathematik und
Physik" in April 2017 (online 15th of February | Optimal decay rate for the wave equation on a square with constant
damping on a strip | optimal decay rate for the wave equation on a square with constant damping on a strip | damped dirichlet square. damping strip. solutions. answers anantharaman eautaud .comment pages. corrected minor mistake formulation revised zeitschrift angewandte mathematik physik april february | non_dup | [] |
42748795 | 10.1007/s00033-017-0803-y | In this paper, we study the multiplicity and concentration of the positive
solutions to the following critical Kirchhoff type problem: \begin{equation*}
-\left(\varepsilon^2 a+\varepsilon b\int_{\R^3}|\nabla u|^2\mathrm{d}
x\right)\Delta u + V(x) u = f(u)+u^5\ \ {\rm in } \ \ \R^3, \end{equation*}
where $\varepsilon$ is a small positive parameter, $a$, $b$ are positive
constants, $V \in C(\mathbb{R}^3)$ is a positive potential, $f \in C^1(\R^+,
\R)$ is a subcritical nonlinear term, $u^5$ is a pure critical nonlinearity.
When $\varepsilon>0$ small, we establish the relationship between the number of
positive solutions and the profile of the potential $V$. The exponential decay
at infinity of the solution is also obtained. In particular, we show that each
solution concentrates around a local strict minima of $V$ as $\varepsilon
\rightarrow 0$ | Multiplicity and concentration behavior of solutions to the critical
Kirchhoff type problem | multiplicity and concentration behavior of solutions to the critical kirchhoff type problem | multiplicity kirchhoff begin varepsilon varepsilon nabla mathrm delta varepsilon mathbb subcritical nonlinearity. varepsilon establish exponential infinity obtained. concentrates strict minima varepsilon rightarrow | non_dup | [] |
73960529 | 10.1007/s00033-017-0808-6 | In this paper we discuss the uniaxial propagation of transient waves within a
semi-infinite viscoelastic Bessel medium. First, we provide the analytic
expression for the response function of the material as we approach the
wave-front. To do so, we take profit of a revisited version of the so called
Buchen-Mainardi algorithm. Secondly, we provide an analytic expression for the
long time behavior of the response function of the material. This result is
obtained by means of the Tauberian theorems for the Laplace transform. Finally,
we relate the obtained results to a peculiar model for fluid-filled elastic
tubes.Comment: 14 pages, 4 figure | On the propagation of transient waves in a viscoelastic Bessel medium | on the propagation of transient waves in a viscoelastic bessel medium | uniaxial propagation transient infinite viscoelastic bessel medium. analytic front. profit revisited buchen mainardi algorithm. secondly analytic material. tauberian theorems laplace transform. relate peculiar filled elastic pages | non_dup | [] |
73956660 | 10.1007/s00033-017-0813-9 | The aim of this paper is to discuss the main result in the paper by D.Y. Gao
and X. Lu [On the extrema of a nonconvex functional with double-well potential
in 1D, Z. Angew. Math. Phys. (2016) 67:62]. More precisely we provide a
detailed study of the problem considered in that paper, pointing out the
importance of the norm on the space $C^{1}[a,b]$; because no norm (topology) is
mentioned on $C^{1}[a,b]$ we look at it as being a subspace of $W^{1,p}(a,b)$
for $p\in [1,\infty]$ endowed with its usual norm. We show that the objective
function has not local extrema with the mentioned constraints for $p\in [1,4)$,
and has (up to an additive constant) only a local maximizer for $p=\infty$,
unlike the conclusion of the main result of the discussed paper where it is
mentioned that there are (up to additive constants) two local minimizers and a
local maximizer. We also show that the same conclusions are valid for the
similar problem treated in the preprint by X. Lu and D.Y. Gao [On the extrema
of a nonconvex functional with double-well potential in higher dimensions,
arXiv:1607.03995].Comment: 12 pages; in this version we added the forgotten condition $F(x) \ne
0$ for $x\in (a,b)$ on page | On D.Y. Gao and X. Lu paper "On the extrema of a nonconvex functional
with double-well potential in 1D" | on d.y. gao and x. lu paper "on the extrema of a nonconvex functional with double-well potential in 1d" | d.y. extrema nonconvex angew. math. phys. precisely pointing norm norm topology look subspace infty endowed usual norm. extrema additive maximizer infty unlike additive minimizers maximizer. valid preprint d.y. extrema nonconvex .comment pages forgotten | non_dup | [] |
73422201 | 10.1007/s00033-017-0814-8 | In this paper, we investigate the global well-posedness of three-dimensional
Navier-Stokes equations with horizontal viscosity under a special symmetric
structure: helical symmetry. More precisely, by a revised Ladyzhenskaya-type
inequality and utilizing the behavior of helical flow, we prove the global
existence and uniqueness of weak and strong solution to the three-dimensional
helical flows. Our result reveals that for the issue of global well-posedness
of the viscous helical fluids, the horizontal viscosity plays the important
role. To some extent, our work can be seen as a generalization of the result by
Mahalov-Titi-Leibovich [Arch. Ration. Mech. Anal. 112 (1990), no. 3, 193-222].Comment: 16 page | Global well-posedness of three-dimensional Navier-Stokes equations with
partial viscosity under helical symmetry | global well-posedness of three-dimensional navier-stokes equations with partial viscosity under helical symmetry | posedness navier stokes viscosity helical symmetry. precisely revised ladyzhenskaya inequality utilizing helical uniqueness helical flows. reveals posedness viscous helical fluids viscosity plays role. generalization mahalov titi leibovich arch. ration. mech. anal. .comment | non_dup | [] |
42691794 | 10.1007/s00033-017-0815-7 | The classical electrodynamic two-body problem has been a long standing open
problem in mathematics. For motion constrained to the straight line, the
interaction is similar to that of the two-body problem of classical
gravitation. The additional complication is the presence of unbounded
state-dependent delays in the Coulomb forces due to the finiteness of the speed
of light. This circumstance renders the notion of local solutions meaningless,
and therefore, straight-forward ODE techniques can not be applied. Here, we
study the time-symmetric case, i.e., the Fokker-Schwarzschild-Tetrode (FST)
equations, comprising both advanced and retarded delays. We extend the
technique developed in \cite{DirkGuenter}, where existence of FST solutions was
proven on the half-line, to ensure global existence -- a result that had been
obtained by Bauer \cite{Bauer} in 1997. Due to the novel technique, the
presented proof is shorter and more transparent but also relies on the idea to
employ asymptotic data to characterize solutions | Global solutions to the electrodynamic two-body problem on a straight
line | global solutions to the electrodynamic two-body problem on a straight line | electrodynamic standing mathematics. constrained straight gravitation. complication unbounded delays coulomb forces finiteness light. circumstance renders notion meaningless straight applied. i.e. fokker schwarzschild tetrode comprising advanced retarded delays. extend cite dirkguenter proven ensure bauer cite bauer shorter transparent relies employ asymptotic characterize | non_dup | [] |
73992176 | 10.1007/s00033-017-0823-7 | We study a scattering on an ultra-low potential in zigzag graphene
nanoribbon. Using mathematical framework based on the continuous Dirac model
and augumented scattering matrix, we derive a condition for the existence of a
trapped mode. We consider the threshold energies where the continuous spectrum
changes its multiplicity and show that the trapped modes may appear for
energies slightly less than a threshold and its multiplicity does not exceeds
one. We prove that trapped modes do not appear outside the threshold, provided
the potential is sufficiently small | Trapped modes in zigzag graphene nanoribbons | trapped modes in zigzag graphene nanoribbons | ultra zigzag graphene nanoribbon. mathematical dirac augumented derive trapped mode. multiplicity trapped multiplicity exceeds one. trapped sufficiently | non_dup | [] |
42693744 | 10.1007/s00033-017-0834-4 | The rotation ${\rm polar}(F) \in {\rm SO}(3)$ arises as the unique orthogonal
factor of the right polar decomposition $F = {\rm polar}(F) \cdot U$ of a given
invertible matrix $F \in {\rm GL}^+(3)$. In the context of nonlinear elasticity
Grioli (1940) discovered a geometric variational characterization of ${\rm
polar}(F)$ as a unique energy-minimizing rotation. In preceding works, we have
analyzed a generalization of Grioli's variational approach with weights
(material parameters) $\mu > 0$ and $\mu_c \geq 0$ (Grioli: $\mu = \mu_c$). The
energy subject to minimization coincides with the Cosserat shear-stretch
contribution arising in any geometrically nonlinear, isotropic and quadratic
Cosserat continuum model formulated in the deformation gradient field $F :=
\nabla\varphi: \Omega \to {\rm GL}^+(3)$ and the microrotation field $R: \Omega
\to {\rm SO}(3)$. The corresponding set of non-classical energy-minimizing
rotations $$
{\rm rpolar}^\pm_{\mu,\mu_c}(F) := \substack{{\rm argmin}\\ R\,\in\,{\rm
SO(3)}}
\Big\{ W_{\mu, \mu_c}(R\,;F) := \mu\, || {\rm sym}(R^TF - 1)||^2 + \mu_c\,
||{\rm skew}(R^TF - 1)||^2 \Big\} $$ represents a new relaxed-polar mechanism.
Our goal is to motivate this mechanism by presenting it in a relevant setting.
To this end, we explicitly construct a deformation mapping $\varphi_{\rm nano}$
which models an idealized nanoindentation and compare the corresponding optimal
rotation patterns ${\rm rpolar}^\pm_{1,0}(F_{\rm nano})$ with experimentally
obtained 3D-EBSD measurements of the disorientation angle of lattice rotations
due to a nanoindentation in solid copper. We observe that the non-classical
relaxed-polar mechanism can produce interesting counter-rotations. A possible
link between Cosserat theory and finite multiplicative plasticity theory on
small scales is also explored.Comment: 28 pages, 11 figure | The relaxed-polar mechanism of locally optimal Cosserat rotations for an
idealized nanoindentation and comparison with 3D-EBSD experiments | the relaxed-polar mechanism of locally optimal cosserat rotations for an idealized nanoindentation and comparison with 3d-ebsd experiments | polar arises orthogonal polar decomposition polar cdot invertible elasticity grioli discovered geometric variational polar minimizing rotation. preceding generalization grioli variational weights grioli minimization coincides cosserat stretch arising geometrically isotropic quadratic cosserat continuum formulated deformation nabla varphi omega microrotation omega minimizing rotations rpolar substack argmin skew relaxed polar mechanism. goal motivate presenting setting. explicitly deformation varphi nano idealized nanoindentation rpolar nano experimentally ebsd disorientation rotations nanoindentation copper. relaxed polar counter rotations. cosserat multiplicative plasticity pages | non_dup | [] |
73399118 | 10.1007/s00033-017-0851-3 | In this paper we consider the one-dimensional Navier-Stokes system for a
heat-conducting, compressible reacting mixture which describes the dynamic
combustion of fluids of mixed kinds on unbounded domains. This model has been
discussed on bounded domains by Chen (SIAM Jour. Math. Anal., 23 (1992),
609--634) and Chen-Hoff-Trivisa (Arch. Rat. Mech. Anal. 166 (2003), 321--358)
among others, in which the reaction rate function is a discontinuous function
obeying the Arrhenius Law. We prove the global existence of weak solutions to
this model on one-dimensional unbounded domains with large initial data in
$H^1$. Moreover, the large-time behaviour of the weak solution is identified
and proved. In particular, the uniform-in-time bounds for the temperature and
specific volume have been established via energy estimates. For this purpose we
utilise techniques developed by Kazhikhov and coauthors ({\it cf.} Siber. Math.
Jour. 23 (1982), 44--49; Jour. Appl. Math. Mech., 41 (1977), 273--282), as well
as a crucial estimate in the recent work by Li-Liang (Arch. Rat. Mech. Anal.
220 (2016), 1195--1208). Several new estimates are also established, in order
to treat the unbounded domain and the reacting terms.Comment: 22 page | On one-dimensional compressible Navier-Stokes equations for a reacting
mixture in unbounded domains | on one-dimensional compressible navier-stokes equations for a reacting mixture in unbounded domains | navier stokes conducting compressible reacting mixture describes combustion fluids kinds unbounded domains. siam jour. math. anal. hoff trivisa arch. rat. mech. anal. discontinuous obeying arrhenius law. unbounded proved. bounds estimates. utilise kazhikhov coauthors siber. math. jour. jour. appl. math. mech. crucial liang arch. rat. mech. anal. treat unbounded reacting | non_dup | [] |
73413611 | 10.1007/s00033-017-0855-z | This paper focuses on the initial- and boundary-value problem for the
two-dimensional micropolar equations with only angular velocity dissipation in
a smooth bounded domain. The aim here is to establish the global existence and
uniqueness of solutions by imposing natural boundary conditions and minimal
regularity assumptions on the initial data. Besides, the global solution is
shown to possess higher regularity when the initial datum is more regular. To
obtain these results, we overcome two main difficulties, one due to the lack of
full dissipation and one due to the boundary conditions. In addition to the
global regularity problem, we also examine the large-time behavior of solutions
and obtain explicit decay rates.Comment: 29 page | On the initial- and boundary-value problem for 2D micropolar equations
with only angular velocity dissipation | on the initial- and boundary-value problem for 2d micropolar equations with only angular velocity dissipation | focuses micropolar dissipation domain. establish uniqueness imposing regularity assumptions data. besides possess regularity datum regular. overcome difficulties dissipation conditions. regularity examine | non_dup | [] |
73987646 | 10.1007/s00033-017-0871-z | The variational heat equation is a nonlinear, parabolic equation not in
divergence form that arises as a model for the dynamics of the director field
in a nematic liquid crystal. We present a finite difference scheme for a
transformed, possibly degenerate version of this equation and prove that a
subsequence of the numerical solutions converges to a weak solution. This
result is supplemented by numerical examples that show that weak solutions are
not unique and give some intuition about how to obtain the physically relevant
solution | A Convergent Finite Difference Scheme for the Variational Heat Equation | a convergent finite difference scheme for the variational heat equation | variational parabolic divergence arises director nematic crystal. transformed possibly degenerate subsequence converges solution. supplemented intuition physically | non_dup | [] |
83847356 | 10.1007/s00033-017-0884-7 | We study the motion of an interface between two irrotational, incompressible
fluids, with elastic bending forces present; this is the hydroelastic wave
problem. We prove a global bifurcation theorem for the existence of families of
spatially periodic traveling waves on infinite depth. Our traveling wave
formulation uses a parameterized curve, in which the waves are able to have
multi-valued height. This formulation and the presence of the elastic bending
terms allows for the application of an abstract global bifurcation theorem of
"identity plus compact" type. We furthermore perform numerical computations of
these families of traveling waves, finding that, depending on the choice of
parameters, the curves of traveling waves can either be unbounded, reconnect to
trivial solutions, or end with a wave which has a self-intersection. Our
analytical and computational methods are able to treat in a unified way the
cases of positive or zero mass density along the sheet, the cases of
single-valued or multi-valued height, and the cases of single-fluid or
interfacial waves.Comment: 29 pages, 4 figure | Periodic traveling interfacial hydroelastic waves with or without mass | periodic traveling interfacial hydroelastic waves with or without mass | irrotational incompressible fluids elastic bending forces hydroelastic problem. bifurcation families spatially traveling infinite depth. traveling formulation parameterized valued height. formulation elastic bending bifurcation type. computations families traveling traveling unbounded reconnect trivial intersection. treat unified sheet valued valued interfacial pages | non_dup | [] |
73384496 | 10.1007/s00033-017-0887-4 | We study the following nonlinear critical curl-curl equation
\begin{equation}\label{eq0.1}\nabla\times \nabla\times U +V(x)U=|U|^{p-2}U+
|U|^4U,\quad x\in \mathbb{R}^3,\end{equation} where $V(x)=V(r, x_3)$ with
$r=\sqrt{x_1^2+x_2^2}$ is 1-periodic in $x_3$ direction and belongs to
$L^\infty(\R^3)$. When $0\not\in \sigma(-\Delta+\frac{1}{r^2}+V)$ and
$p\in(4,6)$, we prove the existence of nontrivial solution for (\ref{eq0.1}),
which is indeed a ground state solution in a suitable cylindrically symmetric
space. Especially, if $ \sigma(-\Delta+\frac{1}{r^2}+V)>0$, a ground state
solution is obtained for any $p\in(2,6)$ | Cylindrically Symmetric Ground State Solutions for Curl-Curl Equations
with Critical Exponent | cylindrically symmetric ground state solutions for curl-curl equations with critical exponent | curl curl begin label nabla nabla quad mathbb sqrt belongs infty sigma delta frac nontrivial cylindrically space. sigma delta frac | non_dup | [] |