Showing papers in "Journal of Differential Equations in 2005"

TL;DR: In this paper, the critical blow-up exponent for a Keller-Segel-type chemotaxis model was determined, where the chemotactic sensitivity equals some nonlinear function of the particle density.

TL;DR: In this article, the authors studied the regularity of weak solutions to the magneto-hydrodynamic equations, which is similar to that of the Navier-Stokes equations.

TL;DR: In this article, all weak traveling wave solutions of the Camassa-Holm equation are classified and shown to have singularities: peakons, cuspons, stumpons, and composite waves.

TL;DR: In this article, the existence of homoclinic orbits for the second order Hamiltonian system q ¨ + V q ( t, q ) = f ( t ), where q ∈ R n and V ∈ C 1 ( R × R n, R ), V ( t, q ) is T-periodic in t.

TL;DR: In this paper, a variant of the deterministic single-substrate chemostat model was introduced and analyzed, where microbe removal and growth rates depend on biomass concentration, with removal terms increasing faster than growth terms.

TL;DR: In this paper, a new definition of a δ -shock wave type solution for a class of systems of conservation laws in the one-dimensional case was introduced, and the weak asymptotics method developed by the authors was used to construct formulas describing the propagation and interaction of δ-shock waves.

TL;DR: In this paper, the authors describe a method to establish existence and regularity of invariant manifolds and, at the same time, find simple maps which are conjugated to the dynamics on them.

TL;DR: In this paper, the authors consider a classical integro-differential equation that arises in various applications as a model for cell-division or fragmentation and prove the existence of a stable steady distribution under general assumptions in the variable coefficients case.

TL;DR: In this article, it was proved that the singular perturbation problem has at least two positive periodic solutions when the anti-maximum principle holds for the Hill operator and the perturbations are superlinear at infinity.

TL;DR: In this article, the existence, uniqueness and continuous dependence on initial data of the solution to a nonlocal Cahn-Hilliard equation on a bounded domain were studied, and a nonlinear Poincare inequality was applied to show the existence of absorbing sets in each constant mass affine space.

TL;DR: In this article, the existence and stability of traveling curved fronts for the Allen-Cahn equation in the two-dimensional space was investigated. And the traveling wave solution between the supersolution and subsolution was shown to be the unique traveling wave solutions between them.

TL;DR: In this article, the authors present a general framework for deriving continuous depen-dence estimates for, possibly polynomially growing, viscosity solutions of fully nonlinear degenerate parabolic integro-PDEs.

TL;DR: In this paper, the authors studied the existence, uniqueness and asymptotic stability of travelling wavefronts of the following equation, where the authors showed that there exists a minimal wave speed c*>0, such that for each c>c* the equation has exactly one travelling wave front U(x+ct) (up to a translation) satisfying U(-∞) = 0,U(+∞)=K and limsupξ→-∞U(ξ)e-Λ1(c)ξ 0 and limx

TL;DR: The reduction of the Heun equation to the hypergeometric equation by polynomial transformations of its independent variable is enumerated and classified in this article, and the conditions for the existence of a reduction involve features of the heun equation that the hyper geometric equation does not possess; namely, its cross-ratio and accessory parameters.

TL;DR: In this article, it was shown that a globally asymptotically stable (GAS) periodic orbit in an autonomous dierence equation must in fact be a fixed point whenever the phase space is connected.

TL;DR: In this article, the authors consider the case that two opposite wave fronts of positive speed approaching each other from both sides of the x-axis and then annihilating in a finite time.

TL;DR: In this article, the expansion of a C0 semigroup and a criterion for being a Riesz basis are discussed, and the heat exchanger problem with boundary feedback is investigated.

TL;DR: In this article, the existence of global attractors is established for different situations: with and without uniqueness, and for both autonomous and non-autonomous cases, using the classical notion of attractor and the recently new concept of pullback one, respectively.

TL;DR: In this article, a class of Stefan-type problems with a convection term and a pseudomonotone nonlinear diffusion operator is considered and the authors prove existence, uniqueness and stability in the framework of renormalized solutions.

TL;DR: In this article, the authors studied the global dynamics of a system of partial differential equations, motivated by modeling the transmission dynamics of infectious diseases in a population with multiple groups and age-dependent transition rates.

TL;DR: In this paper, the regularizing effect of a non-local operator on first-order Hamilton-Jacobi equations was investigated, and it was shown that there exists a unique solution that is C 2 in space and C 1 in time.

TL;DR: In this paper, asymptotic expansions of the solution of the associated Cauchy problem for parabolic partial differential equation are obtained and the desired error bounds are derived and used to analyze related limit distributions of normalized integral functionals.

TL;DR: In this article, the authors extend the Kreiss-Ma jda theory of stability of hyperbolic initial-value and shock problems to a class of systems, notably in-cluding the equations of magnetohydrodynamics (MHD), for which Ma jda's block structure condition does not hold.

TL;DR: In this article, a singularly perturbed convection-diffusion problem on the unit square is considered, and pointwise bounds on the solution and its derivatives are derived by decomposing the solution into a sum of solutions of elliptic boundary-value problems posed on half-planes.

TL;DR: In this article, the KAM machinery is adapted to fit the Schrodinger equation so as to construct small-amplitude periodic or quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system.

TL;DR: In this paper, the authors studied the transition time of smooth singular perturbation problems with C k -normal forms, centre manifolds, and center manifolds of canard solutions.

TL;DR: In this article, the limiting behavior of the least energy solutions for the Henon equation is studied in bounded domains with smooth or non-smooth boundaries. And the effect of the boundary on the limiting profile of the solutions is examined.

TL;DR: In this paper, the authors consider an operator model of the system in Hilbert space and use recent results on the existence of a Riesz basis of invariant finite-dimensional subspaces in order to verify its dissipativity.

TL;DR: In this paper, the authors studied the Schrodinger equation on R 3 × (0, T ), where V 0 (x, t ) = | x - a (t ) | - 1, with a ∈ W 2, 1 ( 0, T ; R 3 ), is a coulombian potential, singular at finite distance, and V 1 is an electric potential, possibly unbounded.