bluuebunny/crossref_metadata_2025_split huggingface dataset:
Existence and regularity results for oblique derivative problems for heat equations in an angle
Authors: Garroni M. G. , Solonnikov V. A. , Vivaldi M. A. 
Published: November 2011

An initial-boundary-value problem is considered for the heat equation in an infinite angle dθr ⊆ R2 × [0, ∞) with the oblique derivative boundary conditions on the faces λi of the angle:with either h0 + h1 > 0, or h0 + h1 ≦ 0. The unique solvability of such a problem is proved in appropriate weighted Sobolev spaces according to the sign of h0 + h1. Estimates of the solution are obtained under ‘natural’ restrictions on the opening of the angle.
A Ginzburg–Landau problem with weight having minima on the boundary
Authors: Beaulieu Anne , Hadiji Rejeb 
Published: November 2011

In this paper, we study the following Ginzburg–Landau functional:where(G, C), andpis a smooth bounded and non-negative map, having minima on the boundary of Ḡ. We give the location of the singularities in the case where the degree around each singularity is equal to 1.
Free quotients of infinite rank of GL2 over Dedekind domains
Authors: Mason A. W. 
Published: November 2011

This paper is concerned with integral domains R, for which the factor group SL2(R)/U2(R) has a non-trivial, free quotient, where U2(R) is the subgroup of GL2(R) generated by the unipotent matrices. Recently, Krstić and McCool have proved that SL2(P[x])/U2(P[x]) has a free quotient of infinite rank, where P is a domain which is not a field. This extends earlier results of Grunewald, Mennicke and Vaserstein.Any ring of the type P[x] has Krull dimension at least 2. The purpose of this paper is to show that result of Krstić and McCool extends to some domains of Krull dimension 1, in particular to certain Dedekind domains. This result, which represents a two-dimensional anomaly is the best possible in the following sense. It is well known that SL2(R) = U2(R), when R is a domain of Krull dimension zero, i.e. when R is a field. It is already known that for some arithmetic Dedekind domains A, the factor group SL2(A)/U2(A) has a free quotient of finite (and not infinite) rank.
Lipschitz regularity of solutions of some asymptotically convex problems
Authors: Raymond Jean-Pierre 
Published: November 2011

SynopsisWe prove local Lipschitz regularity for minimisers of integral functionals of the form J(u) = ∫Ω{f(Du(x)) + g(x, u(x))} dx, where the integrand f is not convex but satisfies some asymptotic convexity assumption.
Behaviour at ±∞ for a model of laminar flames with applications to questions of flame propagation versus extinction
Authors: Avrin Joel D. 
Published: November 2011

SynopsisWe consider the behaviour at x = ±∞ of solutions to reaction-diffusion equations modelling laminar flames in a premixed reactive gas. We show that if the initial data have limits at ±∞, then the solutions satisfy ODEs at ±∞ for all positive time. We then analyse the qualitative behaviour of solutions to the ODEs. Our applications include extensions of previous results on questions of flame propagation versus extinction, and a new decay result: if the initial temperature is above ignition temperature at one end of the domani and if the initial concentration vanishes at the other, then we show that the concentration decays^to zero uniformly as the time variable goes to infinity.
On theKOℤ/2-Euler class, I
Authors: Crabb M. C. 
Published: November 2011

SynopsisThis paper presents a systematic account of ℤ/2-equivariantKO-theoretic methods in the study ofr-fields (that is,rlinearly independent cross-sections,r≧ 1) on a real vector bundle. Applications of the theory to the problem of immersing complex and quaternionic projective spaces in Euclidean space are given in [13].
On the inversion of the even and odd Hilbert transformations
Authors: Heywood P. , Rooney P.G. 
Published: November 2011

SynopsisThe even and odd Hilbert transformations, H+ and H−, are known to be bounded from the power-weighted space ℒμp to itself for −1 < μ 1 and 0 < μ < 2 respectively. We show that they fail to be surjective on ℒ0,p and ℒ1, p respectively, and we characterise the spaces H+(ℒ0, p), H- (ℒ1, p) and find inverses for H+, H− on them.
Integrable spreads and spaces of constant curvature
Authors: Farran H. R. , Robertson S. A. 
Published: November 2011

SynopsisThis paper is a continuation of [2], where we introduced the notion of global k-spreads on manifolds. Here we show that the space of all k-spreads on a manifold has the structure of an affine space, modelled on the vector space of sections of a certain vector bundle. We give some sufficient conditions for a manifold admitting an integrable k-spread to be a space of constant curvature and answer one of the questions raised in [2].
Periodic solutions for: ẋ(t) = λf(x(t),x(t – 1))
Authors: Arino O. , Benkhalti R. 
Published: November 2011

SynopsisWe present a new result on the existence of periodic solutions for the equation:for all positive parameters λ sufficiently large. Our fundamental assumption is the following monotonicity property: if ø ≧ ψ (ø and ψ are data) then x(ø) ≧ x(ψ). The proof consists in applying the global Hopf bifurcation theorem. The main steps are: (i) a classical estimation of the periods; (ii) an a priori estimate for the solutions along a connected branch; (iii) a transformation acting on periodic solutions.
Free generators in relatively free completely regular semigroups
Authors: Trotter P.G. 
Published: November 2011

SynopsisA subset Y of a free completely regular semigroup FCRx freely generates a free completely regular subsemigroup if and only if (i) each -class of FCRx contains at most one element of Y, (ii) {Dy;y ∊ Y} freely generates a free subsemilattice of the free semilattice FCRx/), and (iii) Y consists of non-idempotents. A similar description applies in free objects of some subvarieties of the variety of all completely regular semigroups.
Lower bounds for normal structure coefficients
Authors: Benavides T. Domínguez , Acedo G. López 
Published: November 2011

SynopsisUsing some new expressions for the weakly convergent sequences coefficient WCS(X) the lower boundednessis proved, where δ(-) is the (Clarkson) modulus of convexity. We also define a modulus of noncompact convexity concerning nearly uniformly convex spaces which is used to obtain another lower bound for WCS(X). The computation of this modulus in Ip-spaces shows that our second lower bound is the best possible in these spaces.
Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities
Authors: Galaktionov Victor A. 
Published: November 2011

We present new explicit solutions to some classes of quasilinear evolution equations arising in different applications, including equations of the Boussinesq type:and quasilinear heat equations:The method is based on construction of finite-dimensional linear functional subspaces which are invariant with respect to spatial operators having quadratic nonlinearities. The corresponding nonlinear evolution equations on invariant subspaces are shown to be equivalent to finite-dimensional dynamical systems. Examples of two-, three- and five- dimensional invariant subspaces are given. Some generalisations toN-dimensional quadratic operators are also considered.
Multiparameter bifurcation for some particular reaction–diffusion systems
Authors: Esquinas J. , López-Gómez J. 
Published: November 2011

SynopsisIn some cases, a reaction–diffusion system can be transformed into an abstract equation where the linear part is given by a polynomial of a linear operator, say Multiparameter bifurcation for this equation is considered as the coefficients of the operator polynomial in are varied.
Some existence, uniqueness and nonuniqueness theorems for solutions of parabolic equations with discontinuous nonlinearities
Authors: Feireisl Eduard , Norbury John 
Published: November 2011

SynopsisWe consider the problemwhere H stands for the maximal monotone graph associated with the Heaviside step function. It is shown that the problem possesses at least one (strong) solution belonging to an appropriate function space. Moreover, we prove:(i) There is a smooth initial function u0, u0≧1, where the equality holds at exactly one point such that there are at least two different solutions corresponding to the initial data u0.(ii) The comparison principle: The relation for any x ≠ 0, implies u1(t)>u2(t), t≧0 for any u1, u2 solving the problem with the initial data , respectively.(iii) For a “reasonable” set of initial data the solution is uniquely determined. Moreover, the free boundary {(x, t)| u(x, t) = 1} is regular and on its complement the equation holds in a classical sense.
Phenomena of critical exponent in ℝ2
Authors: Adimurthi  , Srikanth P. N. , Yadava S. L. 
Published: November 2011

SynopsisIn this paper we make an attempt to explain the critical phenomena in ℝ2. We do this by exhibiting a class of functions having growth and for whichdo not admit a solution when R is sufficiently small, where B(R) denotes the ball of radius R in ℝ2.
On the vibrations of rectangular plates
Authors: Haraux Alain , Komornik Vilmos 
Published: November 2011

SynopsisWe prove that, for every non-empty open subset of a rectangular plate, there exists a positive number T such that no vibration of this plate with fixed edges can remain strictly above the rest position at all points of the subset during a period T. Moreover, the result remains valid for every non-empty segment parallel to one of the sides of the plate. Our proof is based on some results of non-harmonic analysis.
Boundary controllability of nonlinear beams to bounded states
Authors: Lagnese J. E. 
Published: November 2011

SynopsisConsidered is a nonlinear model which describes the dynamic behaviour of the not necessarily small longitudinal and transverse displacements of a thin, cantilevered beam. The motion of the beam is driven by a bending moment, an axial force and a vertical shear force that act at the free end of the beam. The main goal is to describe the reachable set of the system, that is, the set of all states that can be reached by varying the end forces within a certain set of admissible controls.
Analytic semigroups generated by ultraweak operators
Authors: Vespri Vincenzo 
Published: November 2011

SynopsisLet Ω be a regular open subset ofRN. We present an improved generation result for nonvariational operators inL1(Ω). This result is obtained by studying ultraweak operators and by proving generation of analytic semigroups inLp(Ω)(l<p≦∞) and in. We also characterise interpolation and extrapolation spaces.
Normal/superconducting transitions in Landau–Ginzburg theory
Authors: Chapman S. J. , Howison S. D. , McLeod J. B. , Ockendon J. R. 
Published: November 2011

SynopsisThe Landau–Ginzburg equations governing a normal/superconducting transition layer are considered. Existence, uniqueness and monotonicity of a solution are proved.
Existence and stability of steady flows of weakly viscoelastic fluids
Authors: Guillopé Colette , Saut Jean-Claude 
Published: November 2011

SynopsisWe consider steady flows of viscoelastic fluids for which the extrastress tensor is given by a differential constitutive equation and is such that the retardation time is large (weaklyviscoelastic fluids).We show the existence of a unique viscoelastic steady flow close to a given Newtonian flow and investigate its linear stability.As an example, we consider the Bénard problem for viscoelastic fluids and we prove that there exists a nontrivial linearly stable flow of a weakly viscoelastic fluid in a container heated from below.
Fibrewise category
Authors: James I. M. , Morris J. R. 
Published: November 2011

SynopsisThe purpose of this paper is to introduce a fibrewise generalisation of category, in the sense of Lusternik–Schnirelmann. This reduces to the classical concept when the space is a point. Fibrewise category may be compared with equivariant category, which has been the subject of some recent research [1,7,8]. Many variations on the basic idea of category have been discussed in the literature, for example the concept of category of a map, but since the generalisations to the fibrewise case are fairly routine they are not considered here.
Multiple homoclinic orbits for autonomous, singular potentials
Authors: Bessi Ugo 
Published: November 2011

We consider the problemwhere u ∊ Rn, n ≧ 2, and V ∊ C2(Rn∖e, R) is a potential having an absolute maximum at 0 and such that V(x) → − ∞ as x → e. We prove that, under some conditions on V, this problem has at least n − 1 geometrically distinct solutions.
Approximation of Young measures by functions and application to a problem of optimal design for plates with variable thickness
Authors: Bonnetier E. , Conca C. 
Published: November 2011

Given a parametrised measure and a family of continuous functions (φn), we construct a sequence of functions (uk) such that, as k→∞, the functions φn(uk) converge to the corresponding moments of the measure,in the weak * topology. Using the sequence (uk) corresponding to a dense family of continuous functions, a proof of the fundamental theorem for Young measures is given.We apply these techniques to an optimal design problem for plates with variable thickness. The relaxation of the compliance functional involves three continuous functions of the thickness. We characterise a set of admissible generalised thicknesses, on which the relaxed functional attains its minimum.
Any large solution of a non-linear heat conduction equation becomes monotonic in time
Authors: Galaktionov Victor A. , Posashkov Sergey A. 
Published: November 2011

SynopsisIn this paper we prove a certain monotonicity in time of non-negative classical solutions of the Cauchy problem for the quasilinear uniformly parabolic equation u1 = (ϕ(u))xx + Q(u) in wT = (0, T] × R1 with bounded sufficiently smooth initial function u(0, x) = uo(x)≧0 in Rl. We assume that ϕ(u) and Q(u) are smooth functions in [0, +∞) and ϕ′(u) >0, Q(u) > 0 for u > 0. Under some additional hypothesis on the growth of Q(u)ϕ′(u) at infinity, it is proved that if u(to, xo) becomes sufficiently large at some point (to, xo) ∈ wT, then ut(t, x0) ≧0 for all t ∈ [t0, T]. The proof is based on the method of intersection comparison of the solution with the set of the stationary solutions of the same equation. Some generalisations of this property for a quasilinear degenerate parabolic equation are discussed.
Localising sets for sigma-algebras and related point transformations
Authors: Lambert Alan 
Published: November 2011

SynopsisEach sigma-finite subalgebra from the sigma-algebra of a measure space induces a conditional expectation operator which acts on L2 as well as the set of almost everywhere nonnegative measurable functions. The concept of localising set is introduced and shown to be closely related to certain functional equations involving . Localising sets are shown to arise naturally in the study of weighted point transformations f→ϕ. f°T, where ϕ is a measurable function and T is a measurable self-map of the state space. A complete characterisation of localising sets related to such transformations is given when the underlying measure space is completely atomic.
On the spectral analysis of self adjoint operators generated by second order difference equations
Authors: Smith Dale T. 
Published: November 2011

SynopsisIn this paper, I shall consider operators generated by difference equations of the formwhere Δ is the forward difference operator, and a, p, and r are sequences of real numbers. The connection between the oscillation constant of this equation and the bottom of the essential spectrum of self-adjoint extensions of the operator generated by the equation is given, as well as various other information about the spectrum of such extensions. In particular, I derive conditions for the spectrum to have only countably many eigenvalues below zero, and a simple criterion for the invariance of the essential spectrum.
On eigencurves of elliptic boundary value problems
Authors: Binding P. A. , Browne P. J. , Huang Y. X. , Picard R. H. 
Published: November 2011

SynopsisLet T be a selfadjoint uniformly elliptic partial differential operator on a bounded domain in Rn, and let S be a (possibly indefinite) L∞ multiplication operator. Estimates of the form σλ + o(λ) and σλ + β + o(1) are sought for the eigenvalues μ(λ) of λS – T as λ→ ±∞. A necessary and sufficient condition is also obtained for existence of linear eigencurves, i.e. μ(λ) = σλ + β.
The existence of infinitely many solutions all bifurcating from λ = 0
Authors: Rother Wolfgang 
Published: November 2011

SynopsisWe consider the non-linear differential equationand state conditions for the function q such that (*) has infinitely many distinct pairs of (weak) solutions such that holds for all k ∈ ℕ. The main tools are results from critical point theory developed by A. Ambrosetti and P. H. Rabinowitz [1].
Radial solutions of a semilinear elliptic problem
Authors: Herrero M. A. , Velázquez J. J. L. 
Published: November 2011

SynopsisWe analyse the set of nonnegative, global, and radial solutions (radial solutions, for short) of the equationwhere 0 < p < 1, and is a radial and almost everywhere nonnegative function. We show that radial solutions of (E) exist if f(r) = o(r2p/1−1−p) or if f(r) ≈ cr2p/1−p as r → ∞, whereWhen f(r) = c*r2p/1−p + h(r) with h(r) = o(r2p/1−p) as r → ∞, radial solutions continue to exist if h(r) is sufficiently small at infinity. Existence, however, breaks down if h(r) > 0,Whenever they exist, radial solutions are characterised in terms of their asymptotic behaviour as r → ∞.
Symmetry breaking for semilinear elliptic equations on sectorial domains in ℝ2
Authors: Lin Song-Sun 
Published: November 2011

SynopsisWe first study the Poisson equation Δu =fin Ώω,and, where Ωω= {(rcos θ,rsin θ): 0<r<1, θ ∈(0,ω)} is a sector in ℝ2, ω ∈ (0, 2π), Г0= {(cos θ, sin θ): θ ∈ (0, ω)} and Г1= ∂Ωω− Г0,band λ are in ℝ1. We obtain Schauder-type estimates and Fredholm alternative theory for the problem. We then study the symmetry breaking problem for the Gel'fand equation Δu+ λeu= 0 in Ωωand obtain a complete picture about the relationships among three parameters λ,b, and ω in the problem.
An ergodic theorem for asymptotically nonexpansive mappings
Authors: Krüppel Manfred , Górnicki Jaroslaw 
Published: November 2011

The purpose of this paper is to prove the following (nonlinear) mean ergodic theorem: Let E be a uniformly convex Banach space, let C be a nonempty bounded closed convex subset of E and let T: C → C be an asymptotically nonexpansive mapping. Ifexists uniformly in r = 0, 1, 2,…, then the sequence {Tnx} is strongly almost-convergent to a fixed point y of T, that is,uniformly in i = 0, 1, 2, ….
Regularisation of Abel's integral equation
Authors: Hai Dang Dinh , Ang Dang Dinh 
Published: November 2011

SynopsisConsider the Abel integral operatorwhere 0 < α < 1. Supposeuis inH1(0, 1) ofH1-norm ≦E, andfis an element ofL2(0, 1) such that ∥Au–f∥L−2< ε. We give a regularised approximate solutionuβ(f) of the equationwhich satisfiesand can be computed simply by performing some integrations. The preceding error estimate can be sharpened by strengthening regularity conditions onu
A class of contracted inverse semigroup rings
Authors: Munn W. D. 
Published: November 2011

SynopsisContracted inverse semigroup rings are studied subject to the restriction that the semilattices of the given inverse semigroups satisfy a certain finiteness condition, introduced in 1980 by Teply, Turman and Quesada. Results are obtained on semiprimitivity, primitivity, primeness, decomposition into a direct sum of ideals, and chain conditions on one-sided ideals.
Periodic solutions of polynomial non-autonomous differential equations
Authors: Devlin J. 
Published: November 2011

Let ℐN denote the set of (N + 1)-tuples of C1 ω-periodic functions; the point P = (pN,…, p1p0) ϵ ℐN is identified with the differential equationWe examine the way in which the total number of ω-periodic solutions can vary as P traverses a path in ℐN.
A note on semiprime Malcev superalgebras
Authors: Elduque Alberto 
Published: November 2011

SynopsisPrime Malcev superalgebras over fields of characteristic not two and three have been studied by Shestakov [8]. He obtains the remarkable result that if these superalgebras have a nonzero odd part then they are Lie superalgebras. The main purpose of this note is to extend this result to fields of characteristic three. To this aim, it is enough to use adequately a result of Filippov [3]. Commutative and anticommutative superalgebras will be considered too, showing that they are prime, semiprime or simple as superalgebras if and only if they are as algebras. Finally, some conclusions for finite-dimensional semisimple Malcev superalgebras will be deduced. Any such superalgebra is the direct sum of a semisimple Lie superalgebra and a direct sum of simple non-Lie algebras.
Existence and finite dimensionality of the global attractor for a class of nonlinear dissipative equations
Authors: Alarcón Eduardo Arbieto 
Published: November 2011

SynopsisIn this work we discuss the Cauchy problem for a class of nonlinear dissipative equations as well as the existence of a global attractor and we estimate its dimension in the sense of the Hausdorff (or fractal) dimension.
Hofer–Zehnder symplectic capacity for two-dimensional manifolds
Authors: Jiang Mei-Yue 
Published: November 2011

SynopsisIn this paper, we show that the Hofer-Zehnder symplectic capacity of a two-dimensional manifold is same as the area of the manifold. Using this fact, we also get a result on the symplectic capacity of the cotangent bundle of the torus with its canonical symplectic form.
Isoperimetric bounds for higher eigenvalue ratios for the n-dimensional fixed membrane problem
Authors: Ashbaugh Mark S. , Benguria Rafael D. 
Published: November 2011

SynopsisWe give several results which extend our recent proof of the Payne-Pólya–Weinberger conjecture to ratios of higher eigenvalues. In particular, we show that for a bounded domain Ω⊂ℝn the eigenvalues of its Dirichlet Laplacian obey where λm denotes the mth eigenvalue and jp,k denotes the kth positive zero of the Bessel function Jp(x). Certain extensions of this result are given, the most general being the bound where k≧2 and l(m) denotes the number of nodal domains of an mth eigenfunction. Our results imply certain further conjectures of Payne, Pólya, and Weinberger concerning λ3/λ2 and λ4/λ3. In addition, we find a resonably good bound on λ4/λ1. We also briefly discuss extensions to Schrödinger operators and other elliptic eigenvalue problems.
First-order elliptic systems degenerated at the boundary
Authors: Dzhuraev Abduhamid 
Published: November 2011

SynopsisIn this paper we state that the bounded solutions of general first order linear elliptic systems of two equations in bounded multiply-connected plane domains, degenerated at the boundary, are determined in domains without any boundary conditions, provided the boundary is not characteristic for this system. The explicit formula for calculating the index of the system is derived.
On the stability of the saddle solution of Allen–Cahn's equation
Authors: Schatzman M. 
Published: November 2011

Letfbe an odd,C2function on [− 1, 1], which vanishes at ± 1, and such thatf′(O) < 0,f′ (±1) > 0 andu↦f(u)/uis increasing. Dang, Fife and Peletier [5] showed that there is a unique solutionuwith values in [−1, 1] ofwhich has the same sign asxy. The linearised operator arounduisBdefined byIt is proved here that the spectrum of B contains at least one negative eigenvalue, that all eigenfunctions corresponding to negative eigenvalues have the symmetries of the square, and that for Allen–Cahn's nonlinearity (f(u) = 2u3− 2u), there is exactly one negative eigenvalue.