Showing papers in "Journal of Differential Equations in 2010"

TL;DR: In this article, the authors considered the classical parabolic-parabolic Keller-Segel system with homogeneous Neumann boundary conditions in a smooth bounded domain and proved that for each q > n 2 and p > n one can find e 0 > 0 such that if the initial data ( u 0, v 0 ) satisfy L q ( Ω ) e and ∇ v 0 ‖ L p (Ω) e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic

TL;DR: In this paper, a systematic approach that allows one to construct global Lyapunov functions for large-scale coupled systems from building blocks of individual vertex systems is presented. But the approach is applied to several classes of coupled systems in engineering, ecology and epidemiology, and is shown to improve existing results.

TL;DR: In this article, the existence of positive solutions for the Schrodinger-Poisson system with nonnegative functions has been proved, but not requiring any symmetry property on them and satisfying suitable assumptions.

TL;DR: In this article, the authors established regularity criteria for the 3D incompressible MHD equations in terms of the derivative of the velocity field in one direction and the boundedness of the pressure in another direction.

TL;DR: In this article, the Hopf bifurcation problem for non-smooth planar systems was studied and it was shown that one or two limit cycles can be produced from an elementary focus of the least order (order 1 for FF or FP type and order 2 for PP type).

TL;DR: In this paper, a principal eigenvalue theory for nonlocal dispersal operators with space periodic dependence is developed, which plays an important role in the study of spreading speeds of nonlocal periodic monostable equations and is also of independent interest.

TL;DR: In this paper, it was shown that the ill-posedness of the inverse source problem decreases as the frequency increases and under some regularity assumptions on the source function, the logarithmic stability converts to a linear one for the inverse problem.

TL;DR: In this article, a new global existence result and several new blow-up results of strong solutions to the system were presented, and the results for the system are sharp and improve considerably earlier results.

TL;DR: In this article, the existence of a principal eigenfunction of a nonlocal operator which appears in the description of various phenomena ranging from population dynamics to micro-magnetism was studied.

TL;DR: In this paper, the authors combine techniques from geometric singular perturbation theory (the blow-up technique) and from delayed Hopf bifurcation theory (complex time path analysis) to analyze the flow near folded saddle-nodes.

TL;DR: In this article, the stack of iterated integrals of a path is embedded in a larger algebraic structure where iterated integral are indexed by decorated rooted trees and where an extended Chen's multiplicative property involves the Durr-Connes-Kreimer coproduct on rooted trees.

TL;DR: In this paper, the authors established the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth by using a change of variables, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem.

TL;DR: In this paper, the authors study a fractional diffusion Boussinesq model which couples a Navier-Stokes type equation with fractional flow for the velocity and a transport equation for the temperature.

TL;DR: In this article, the authors considered the case d ∗ = 0 and obtained necessary and sufficient conditions for the operators H X, α to be self-adjoint, lower semibounded, and discrete.

TL;DR: A traffic flow model describing the formation and dynamics of traffic jams was introduced by Berthelin et al., which consists of a constrained pressureless gas dynamics system and can be derived from the Aw-Rascle model under the constraint condition p <= p* by letting the traffic pressure vanish.

TL;DR: In this article, the authors studied the large-time behavior of solutions of one-dimensional Fisher-KPP reaction diffusion equations with slowly decaying initial conditions and proved that all level sets of the solutions move infinitely fast as time goes to infinity.

TL;DR: In this article, the authors prove the global existence and uniqueness of smooth solutions to the 2D micropolar fluid flows with zero angular viscosity and prove that smooth solutions are the only solutions that have zero angular viscosity.

TL;DR: Chemin and Masmoudi as discussed by the authors improved the Chemin criterion for regular solutions of equations related to viscoelastic fluids and provided a new method to prove and improve it.

TL;DR: In this paper, a class of integral equations without monotonicity is investigated, and it is shown that there is a spreading speed c ∗ > 0 for such an integral equation, and that its limiting integral equation admits a unique traveling wave (up to translation) with speed c ⩾c ∗ and no traveling wave with c c c ∆.

TL;DR: In this article, the global regularity of classical solutions to the 2D Boussinesq equations with vertical dissipation and vertical thermal diffusion was investigated and it was shown that the L r -norm of the vertical velocity v for any 1 0 would guarantee the global norm of the classical solutions.

TL;DR: In this article, the analysis of measure-valued solutions to a nonlinear structured population model given in the form of a nonlocal first-order hyperbolic problem on R +.

TL;DR: In this paper, the authors studied the well-posedness issue for the density-dependent Euler equations in the whole space and established local-in-time results for the Cauchy problem pertaining to data in the Besov spaces embedded in the set of Lipschitz functions.

TL;DR: In this article, the Cauchy problem of the Navier-Stokes-Poisson equations in multi-dimensions (n ⩾ 3 ) is considered and the pointwise estimates of the solution when it is a perturbation of the constant state are obtained.

TL;DR: In this paper, the pseudoparabolic equation was investigated and the existence of the traveling wave type solutions was extensively studied, however, the existence seems to be known only for the nondegenerate case, when k is strictly positive.

TL;DR: In this paper, the authors prove the well-posedness of a renormalized solution to nonlinear parabolic equations with variable exponents and L 1 -data in the functional setting.

TL;DR: In this article, the wave equation with supercritical interior and boundary sources and damping terms is considered and local Hadamard well-posedness of finite energy solutions is obtained.

TL;DR: In this article, the existence and uniqueness of local in time strong solution with large initial data for the three-dimensional compressible viscoelastic flow was established and the strong solution has weaker regularity than the classical solution.

TL;DR: In this paper, a sufficient condition on the existence of homoclinic solutions of a class of discrete nonlinear periodic systems was obtained by using critical point theory in combination with periodic approximations.

TL;DR: In this article, the authors discuss the existence and multiplicity of positive solutions of the prescribed mean curvature problem − div ( ∇ u / 1 + | ∇ n | 2 ) = λ f ( x, u ) in Ω, u = 0 on ∂ Ω, in a general bounded domain Ω ⊂ R N, depending on the behavior at zero or at infinity of f (x, s ), or of its potential F ( x, s ) = ∫ 0 s f( x, t ) d t.

TL;DR: In this paper, sufficient conditions for the existence of a solution to the problem u ∈ [0, ω ], u ( 0 ) = u ( ω ), u ǫ ( 0) = uǫ( ω ).