bluuebunny/crossref_metadata_2025_split huggingface dataset:
Heteroclinic orbits between rotating waves in hyperbolic balance laws
Authors: Härterich Jörg 
Published: November 2011

We deal with the large-time behaviour of scalar hyperbolic conservation laws with source termswhich are often called hyperbolic balance laws. Fan and Hale have proved existence of a global attractorfor this equation withx∈S1.consists of spatially homogeneous equilibria, a large number of rotating waves and of heteroclinic orbits between these objects. In this paper, we solve the connection problem and show which equilibria and rotating waves are connected by a heteroclinic orbit. Apart from existence results, our approach via generalized characteristics also gives geometric information about the heteroclinic solutions, e.g. about the shock curves and their strength.
The effective bulk energy of the relaxed energy of multiple integrals below the growth exponent
Authors: Bouchitté Guy , Fonseca Irene , Malý Jan 
Published: November 2011

The characterisation of the bulk energy density of the relaxation inW1, P(Ω; ℝd) of a functionalis obtained forp>q–q/N, whereu∈W1,P(Ω; ℝd), andfis a continuous function on the set ofd × Nmatrices verifyingfor some constantC> 0 and 1 ≦q< + ∞. Typical examples may be found in cavitation and related theories. Standard techniques cannot be used due to the gap between the exponentqof the growth condition and the exponent p of the integrability of the macroscopic strain ∇u. A recently introduced global method for relaxation and fine Sobolev trace and extension theorems are applied.
On subordinacy and spectral multiplicity for a class of singular differential operators
Authors: Gilbert D. J. 
Published: November 2011

The spectral multiplicity of self-adjoint operatorsHassociated with singular differential expressions of the formis investigated. Based on earlier work of I. S. Kac and recent results on subordinacy, complete sets of necessary and sufficient conditions for the spectral multiplicity to be one or two are established in terms of: (i) the boundary behaviour of Titchmarsh–Weylm-functions, and (ii) the asymptotic properties of solutions ofLu= λu, λ∈ℝ, at the endpointsaandb. In particular, it is shown thatHhas multiplicity two if and only ifLis in the limit point case at bothaandband the set of all λ for which no solution ofLu= λuis subordinate at eitheraorbhas positive Lebesgue measure. The results are completely general, subject only to minimal restrictions on the coefficientsp(r), q(r)andw(r), and the assumption of separated boundary conditions whenLis in the limit circle case at both endpoints.
A semilinear heat equation with singular initial data
Authors: Kwak Minkyu 
Published: November 2011

We first prove existence and uniqueness of non-negative solutions of the equationin in the range 1 < p < 1 + 2/N, when initial data u(x, 0) = a|x|−2(p−1), x ≠ 0, for a > 0. It is proved that the maximal and minimal solutions are self-similar with the formwhere g = ga satisfiesAfter uniqueness is proved, the asymptotic behaviour of solutions ofis studied. In particular, we show thatThe case for a = 0 is also considered and a sharp decay rate of the above equation is derived. In the final, we reveal existence of solutions of the first and third equations above, which change sign.
Schützenberger groups of polynomials in the semigroup of entire functions
Authors: Magill K. D. 
Published: November 2011

SynopsisLet denote the semigroup, under composition, of all entire functions of a complex variable and for , let Γ(f) denote the Schützenberger group of the ℋ-class of which contains f. The main results of this paper completely describe Γ(P) where P is a polynomial function. Γ(P) is trivial if P is a constant function. If Deg (P) (the degree of P) is one, then Γ(P) is isomorphic to the group of all matrices of the form where a and b are complex numbers with a ≠ 0. If Deg (P) > 1, then Γ(P) is isomorphic to ℂM, the multiplicative group of nonzero complex numbers if and only if P(z) = α(z +β)n + γ where α ≠ 0. If P is not of this form and Deg (P) > 1, then Γ (P)is a finite cyclic group and its order can be determined by defining (where αn−1 and α n are the coefficients in P of zn−1 and zn respectively) and then inspecting the coefficients of Q.
On the asymptotics of a Wiener integral
Authors: van den Berg M. , Lewis J. T. 
Published: November 2011

SynopsisLet mt(ω) be the range of a standard brownian bridge on R with ω(0) = ω(t) = 0 and let µt(ω) be the corresponding Wiener measure. We determine the asymptotic behaviour for large t of ∫ e−G(mt(ω)) µt(dω) for an increasing convex function G.
Low energy resolvent estimates and continuity of time-delay operators
Authors: Xue-Ping Wang 
Published: November 2011

SynopsisIn this paper, we are interested in the L2-continuity of the Eisenbud–Wigner time-delay operator in potential scattering theory. Using the ideas due to Jensen–Kato [5], we first establish some low energy estimates on the resolvent of the Schrödinger operator and its derivative in weighted Sobolev spaces. Then applying these results together with the global decay of the wave functions (Lemma 3.2), we show that the Eisenbud–Wigner time-delay operator extends to a bounded operator on L2(Rn) with n ≧ 4, on condition that the potential V(x) decreases as fast as 0(|x | −4−ε) at infinity and that 0 is neither the eigenvalue nor the resonance for the Schrodinger operator –Δ + V for n = 4 or 5.
Conjugacy classes in finite groups
Authors: López Antonio Vera 
Published: November 2011

SynopsisIn this paper, the number of conjugacy classes in a finite group G is analysed in terms of the number of ordered pairs that generate it. Using this relation, we give a new elementary proof of one of A. Mann's results for finite groups, namely: |G| ≡ r(G) (mod. d|G|. δ|G|), where , prime and pi ≠ Pj for every i≠j, r(G) denotes the number of conjugacy classes of elements of G, d|G| = g.c.d. (p1 − 1, … pt − 1) and δ|G| = g.c.d. . The above congruence is obtained without using character theory. We also obtain new local congruences that slightly improve Mann's congruence.
Global existence and convergence to a singular steady state for a semilinear heat equation
Authors: Lacey A.A. , Tzanetis D. 
Published: November 2011

SynopsisWith certain initial and boundary conditions the solution u* to the semilinear heat equation ∂u*/∂t = ∂u* + λ * f(u*), where f is a positive superlinear function and λ is the supremum of the open spectrum for the steady state problem Δw + λf(w) = 0, is found to exist for all time and to be unbounded. Moreover u* approaches w* a singular steady state, as / tends to infinity.
Conformal maps in methods of asymptotic continuation
Authors: Gingold H. 
Published: November 2011

SynopsisTake the coefficients of a Taylor series expansion of a holomorphic function about its regular point zR. It is known that the holomorphic function possesses an asymptotic expansion about a possibly singular point zs. We show how to construct and calculate the coefficients in the asymptotic expansion from the coefficient of the Taylor series. The main theorem demonstrates that a suitable conformal map is a decisive step in dealing with the problem above. Therefore, a suitable conformal map is critical to a successful summation of divergent series. Some other methods which utilise orthogonal polynomial and Cesaro summability are also discussed. The paper may serve as a theoretical basis for a new computational method.
Periodic solutions of forced Liénard equations with jumping nonlinearities under nonuniform conditions
Authors: Iannacci R. , Nkashama M.N. , Omari P. , Zanolin F. 
Published: November 2011

SynopsisThis paper is devoted to the existence of periodic solutions for the scalar forced Lienard differential equationThe key assumptions relate the asymptotic behaviour asx→± ∞ofg(t;x)/xto the “critical values” of the positively 1-homogeneous problemNo condition onf, except continuity, is assumed. Our approach is based on Leray–Schauder degree techniques anda prioriestimates.
A dual method in the calculation of homogenisation and applications
Authors: Qi Tang 
Published: November 2011

SynopsisWe give a new method for calculating the Γ-limit functional encountered in the problems of homogenisation. We use the Legendre–Lagrange transform in the convex analysis and regularisation method to obtain the explicit expression of the Γ-limit functional. The result can be applied to some nonlocal function spaces.
On the convolution operators arising in the study of abstract initial boundary value problems
Authors: Alonso-Mallo I. , Palencia C. 
Published: November 2011

We consider convolution operators arising in the study of abstract initial boundary value problems. These operators are of the formwhere {S(t)}t ≧0 is a C0-semigroup in a Banach space X,, with infinitesimal generator A0,: D(A0), ⊂ X, → X, and K(z): Y → X is a linxear, continuous mapping defined in another Banach space Y., We study the continuity of T between the spaces Lp([0, + ∞), Y), and Lq([0, + ∞), X), 1 ≦ p, q, ≦ + ∞. We give several examples of the applicability of the results to some familiar initial boundary value problems, including both parabolic and hyperbolic cases.
Three-phase boundary motions under constant velocities. I: The vanishing surface tension limit
Authors: Reitich Fernando , Soner H. Mete 
Published: November 2011

In this paper, we deal with the dynamics of material interfaces such as solid–liquid, grain or antiphase boundaries. We concentrate on the situation in which these internal surfaces separate three regions in the material with different physical attributes (e.g. grain boundaries in a polycrystal). The basic two-dimensional model proposes that the motion of an interface Гij between regions i and j (i, j = 1, 2, 3, i ≠ j) is governed by the equationHere Vij, kij, μij and fij denote, respectively, the normal velocity, the curvature, the mobility and the surface tension of the interface and the numbers Fij stand for the (constant) difference in bulk energies. At the point where the three phases coexist, local equilibrium requires thatIn case the material constants fij are small, and ε ≪ 1, previous analyses based on the parabolic nature of the equations (0.1) do not provide good qualitative information on the behaviour of solutions. In this case, it is more appropriate to consider the singular case with fij = 0. It turns out that this problem, (0.1) with fij = 0, admits infinitely many solutions. Here, we present results that strongly suggest that, in all cases, a unique solution—‘the vanishing surface tension (VST) solution’—is selected by letting ε→0. Indeed, a formal analysis of this limiting process motivates us to introduce the concept of weak viscosity solution for the problem with ε = 0. As we show, this weak solution is unique and is therefore expected to coincide with the VST solution. To support this statement, we present a perturbation analysis and a construction of self-similar solutions; a rigorous convergence result is established in the case of symmetric configurations. Finally, we use the weak formulation to write down a catalogue of solutions showing that, in several cases of physical relevance, the VST solution differs from results proposed previously.
The limit of the anisotropic double-obstacle Allen–Cahn equation
Authors: Elliott Charles M. , Schätzle Reiner 
Published: November 2011

In this paper, we prove that solutions of the anisotropic Allen–Cahn equation in doubleobstacle formwhere A is a strictly convex function, homogeneous of degree two, converge to an anisotropic mean-curvature flowwhen this equation admits a smooth solution in ℝn. Here VN and R respectively denote the normal velocity and the second fundamental form of the interface, and More precisely, we show that the Hausdorff-distance between the zero-level set of φ and the interface of the above anisotropic mean-curvature flow is of order O(ε2).
Resolution of the spherical piston problem for compressible isentropic gas dynamics via a self-similar viscous limit
Authors: Slemrod M. 
Published: November 2011

This paper proves the existence of solutions to the spherical piston problem for isentropic gas dynamics with equation of state p(p) = Apγ, γ≧ 1. The method of analysis is to replace the usual viscosity ε with εt, thus permitting a search for self-similar viscous limits. The main result of the paper is that self-similar viscous limits are proved to exist and converge to a solution to the piston problem whenN = 1, 2, 3 space dimensions.
Compactness and single-point blowup of positive solutions on bounded domains
Authors: Filippas Stathis , Merle Frank 
Published: November 2011

This paper is concerned with the blowup of positive solutions of the semilinear heat equationwith zero boundary conditions. The domainΩis supposed to be smooth, convex and bounded. We first show that, under the assumption that the initial data are uniformly monotone near the boundary, solutions that exist on the time interval (0,Tform a compact family in a suitable topology. We then derive some localisation properties of these solutions. In particular, we discuss a general criterion, independent of the initial data, which in some cases ensures single-point blowup.
Diffusion-mediated permanence problem for a heterogeneous Lotka–Volterra competition model
Authors: Furter J. E. , López-Gómez J. 
Published: November 2011

We analyse the dynamics of a prototype model for competing species with diffusion coefficients (d1d2) in a heterogeneous environment Ω. When diffusion is switched off, at each pointx∊ Ω we have a pair of ODE's: thekinetic. If for somex∊ Ω kinetic has a unique stable coexistence state, we show that there existsuch that for everythe RD-model ispersistent, in the sense that it has a compact global attractor within the interior of the positive cone and has a stable coexistence state. The same result is true if there existxu,xv∊ Ω such that the semitrivial coexistence states (u, 0) and (0,v) of thekineticare globally asymptotically stable atx=xuandx=xv, respectively. More generally, our main result shows that, for most kinetic patterns, stable coexistence of xspopulations can be found for some range of the diffusion coefficients.Singular perturbation techniques, monotone schemes, fixed point index, global analysis ofpersistence curves, global continuation and singularity theory are some of the technical tools employed to get the previous results, among others. These techniques give us necessary and/or sufficient conditions for the existence and uniqueness of coexistence states, conditions which can be explicitly evaluated by estimating some principal eigenvalues of certain elliptic operators whose coefficients are solutions of semilinear boundary value problems.We also discuss counterexamples to the necessity of the sufficient conditions through the analysis of the local bifurcations from the semitrivial coexistence states at the principal eigenvalues. An easy consequence of our analysis is the existence of models having exactly two coexistence states, one of them stable and the other one unstable. We find that there are also cases for which the model hasthree or morecoexistence states.
Weak asymptotic decay via a “relaxed invariance principle” for a wave equation with nonlinear, non-monotone damping
Authors: Slemrod M. 
Published: November 2011

SynopsisThis paper considers the problem of asymptotic decay as t → ∞ of solutions of the wave equation utt − Δu = −a(x)β(ut, ∇u), (t,x) ∊ ℝ+ × Ω (a bounded, open, connected set in ℝN, N≧ 1, with smooth boundary), u =0 on ℝ+ × ∂Ω. The nonlinear function β is not assumed to be globally Lipschitz continuous, β(0, y2, …, yN+1) = 0, y1 β(y1…,yN+1) ≧ 0 for all y ∊ ℝN+1; β is not assumed to be monotone in y1. Under additional restrictions on the kernel of β, conditions are given which imply that [u, ut,] converges to [0,0] weakly in H = H10(Ω) × L2(Ω) as t → ∞. The work generalises earlier results of Dafermos and Haraux where strong decay in H as t → ∞ was obtained in the case β(y1 …, yN+1) = q(y1), q monotone on ℝ.
The displacement problem for elastic crystals
Authors: Fonseca I. , Tartar L. 
Published: November 2011

SynopsisIn this paper we obtain necessary and sufficient conditions for the existence of Lipschitz minimisers of a functional of the typewhere h is a convex function converging to infinity at zero and u is subjected to displacement boundary conditions. We provide examples of body forces f for which the infimum of J(.) is not attained.
A differential equation in the theory of resonant oscillations of water waves
Authors: Amick C. J. , Toland J. F. 
Published: November 2011

SynopsisWe show that the problemhas a unique solution and that the asymptotic behaviour of this solution as x → −∞ is given by w(x) = x + B ∣x∣−1/4 cos (b ∣x∣3/2 + φ) + O(x−1), for some constant φ. Here B ≠ 0 depends on ε and In particular there are no even solutions of problem (*) for any ε > 0.
Nonexistence of radial solutions of two elliptic boundary value problems
Authors: Ortega Rafael 
Published: November 2011

SynopsisWe consider two boundary value problems (of Neumann or related type) associated with the equationin Ω. The existence of a solution was previously established assuming thatp<N/(N−s2). (Ndimension of Ω.) We prove that this exponent is critical for these problems, at least in the radially symmetric case when Ω is a ball. This is understood in the sense that the existence result does not hold whenp≧N/(N− 2).
Almost periodic solutions in an integrodifferential equation
Authors: Hamaya Y. , Yoshizawa T. 
Published: November 2011

SynopsisWe consider a system of integrodifferential equationswheref(t,x) andF(t,s,x,y) are almost periodic intuniformly for parameters, and we assume that the system has a bounded solutionu(t). To discuss the existence of an almost periodic solution, we consider the relationship between the total stability ofu(t) with respect to a certain metric ρ and the separation condition with respect to ρ. Moreover, we discuss a sufficient condition for the existence of a positive almost periodic solution of a model of the dynamics of ann-species system.
Idempotent rank in finite full transformation semigroups
Authors: Howie John M. , McFadden Robert B. 
Published: November 2011

SynopsisThe subsemigroup Singn of singular elements of the full transformation semigroup on a finite set is generated by n(n − l)/2 idempotents of defect one. In this paper we extend this result to the subsemigroup K(n, r) consisting of all elements of rank r or less. We prove that the idempotent rank, defined as the cardinality of a minimal generating set of idempotents, of K(n, r) is S(n, r), the Stirling number of the second kind.
Existence and stability of travelling wave solutions for an evolutionary ecology model
Authors: Lui Roger 
Published: November 2011

SynopsisMonotone travelling wave solutions are known to exist for Fisher's equation which models the propagation of an advantageous gene in a single locus, two alleles population genetics model. Fisher's equation assumed that the population size is a constant and that the fitnesses of the individuals in the population depend only on their genotypes. In this paper, we relax these assumptions and allow the fitnesses to depend also on the population size. Under certain assumptions, we prove that in the second heterozygote intermediate case, there exists a constant θ*>0 such that monotone travelling wave solutions for the reaction–diffusion system exist whenever θ > θ*. We also discuss the stability properties of these waves.
On the topological properties of symplectic maps
Authors: Hofer H. 
Published: November 2011

SynopsisIn this paper we show that symplectic maps have surprising topological properties. In particular, we construct an interesting metric for the symplectic diffeomorphism groups, which is related, but not obviously, to the topological properties of symplectic maps and phase space geometry. We also prove a certain number of generalised symplectic fixed point theorems and give an application to a Hamiltonian system.
Compact attractor for a nonlinear wave equation with critical exponent
Authors: Lopes Orlando 
Published: November 2011

SynopsisIn this paper we study the existence of a compact attractor for the solutions of the equation utt − Δu + cut + f(u) = h(t, x), x ∊ ℝ3. The phase space is H1 × L2 and periodicity in the x-variables is taken as a boundary condition. Besides the usual coercive condition, we assume f satisfies the growth condition |f′(u)|≦ a + bu2; this growth condition is critical because the embedding H1 → L6 is not compact. In the proof we use an Lp − H1.q estimate for the linear homogeneous wave equation.
Nonlinear analytic semiflows
Authors: Angenent Sigurd B. 
Published: November 2011

SynopsisIn this paper a local existence and regularity theory is given for nonlinear parabolic initial value problems (x′(t) = f(x(t))), and quasilinear initial value problems (x′(t)=A(x(t))x(t) + f(x(t))). This theory extends the theory of DaPrato and Grisvard of 1979, and shows how various properties, like analyticity of solutions, can be derived as a direct corollary of the existence theorem.
On contracted semigroup rings
Authors: Munn W. D. 
Published: November 2011

SynopsisSufficient conditions are given for a contracted semigroup ring, in which the two-sided ideals have a certain property, to be (a) semiprime, (b) semiprimitive, (c) prime, (d) primitive. The results are applied to the contracted semigroup rings of inverse semigroups, where they provide new proofs of theorems of Domanov.
Noncoercive variational inequalities with application to friction problems
Authors: Shi P. , Shillor M. 
Published: November 2011

SynopsisNoncoercive variational inequalities with sublinear functionals are considered. Necessary and sufficient conditions are given for the solvability of such problems. These conditions are in the form of compatibility conditions-for the data, as well as the boundedness of the solutions to related problems. These results are used for the obstacle problems for the membrance and the elastic contact in the presence of friction.
Symplectic connections and the linearisation of Hamiltonian systems
Authors: Marsden J. E. , Ratiu T. , Raugel G. 
Published: November 2011

SynopsisThis paper uses symplectic connections to give a Hamiltonian structure to the first variation equation for a Hamiltonian system along a given dynamic solution. This structure generalises that at an equilibrium solution obtained by restricting the symplectic structure to that point and using the quadratic form associated with the second variation of the Hamiltonian (plus Casimir) as energy. This structure is different from the well-known and elementary tangent space construction. Our results are applied to systems with symmetry and to Lie–Poisson systems in particular.
On perturbations of a translationally-invariant differential equation
Authors: Magnus R.J. 
Published: November 2011

SynopsisWe study certain perturbations of the differential equation Δu − u + up = 0 on all of n-dimensional Euclidean space. Conditions are obtained which ensure the existence of a solution to the perturbed equation near a given solution to the unperturbed equation. We have to overcome degeneracy of the unperturbed solution and lack of smooth dependence on the perturbation parameter. An abstract version of the argument is sketched in a functional-analytic setting related toequivariant bifurcation theory. We consider also a smooth perturbation with several parameters and study the singularities of the mapping which maps each solution to its associated parameters.
Equichordal curves
Authors: Carvalho F.J.Craveiro de , Robertson S.A. 
Published: November 2011

SynopsisIn this paper we extend the notion of equichordal curve to closed simple curves in ℝn. Although it is not known if an equichordal curve can have more than one fulcrum, we show that, for plane curves, any fulcrum is inside the curve. We establish connections with the theories of transnormal and self-parallel curves and lower bounds for the length and chordal area are obtained. Such bounds are the best possible.