Showing papers in "Journal of Differential Equations in 2012"

TL;DR: For the quasilinear parabolic Keller-Segel system with homogeneous Neumann boundary conditions, this article showed that the classical solutions to the problem are uniformly in time bounded, provided that D ( u ) satisfies some technical conditions such as algebraic upper and lower growth estimates as u → ∞.

TL;DR: In this article, the existence, multiplicity and concentration behavior of positive solutions for the nonlinear Kirchhoff type problem is studied, where V is a positive continuous potential satisfying some conditions and f is a subcritical nonlinear term.

TL;DR: In this paper, the authors studied the effect of lower order perturbations in the existence of positive solutions to the critical elliptic problem involving the fractional Laplacian.

TL;DR: The existence of a positive solution to a Kirchhoff type problem on R N is proved by using variational methods, and the new result does not require usual compactness conditions as discussed by the authors.

TL;DR: In this paper, the authors studied pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with nonautonomous deterministic as well as stochastic forcing terms.

TL;DR: In this article, the multiplicity and concentration of positive solutions for the semilinear Kirchhoff type equation were studied and the relation between the number of positive ground state solutions and the topology of the set of the global minima of the potentials by minimax theorems and the Ljusternik-Schnirelmann theory was investigated.

TL;DR: In this paper, it was shown that for arbitrarily large initial data, this problem admits at least one global weak solution for which there exists T > 0 such that ( u, v ) is bounded and smooth in Ω × (T, ∞ ).

TL;DR: In this article, the authors considered quasilinear Keller-Segel type systems of two kinds in higher dimensions and proved an optimal (with respect to possible nonlinear diffusions generating explosion in finite time of solutions) finite-time blowup result.

TL;DR: In this paper, the existence and uniqueness of mild solutions and classical solutions to the Cauchy problem for linear and semilinear time fractional evolution equations involving in the linear part, a linear operator A whose resolvent satisfies the estimate of growth −γ ( − 1 γ 0 ) in a sector of the complex plane, which occurs when one considers the partial differential operators in the limit domain of dumb-bell with a thin handle or in the space of Holder continuous functions.

TL;DR: In this paper, sufficient conditions are established for the approximate controllability of a class of semilinear delay control systems of fractional order, and the existence and uniqueness of mild solution of the system is also proved.

TL;DR: In this paper, the authors derived an averaged equation for a class of stochastic partial differential equations without any Lipschitz assumption on the slow modes and derived the rate of convergence in probability as a byproduct.

TL;DR: In this paper, the authors considered the Timoshenko beam model with second sound and showed that the corresponding semigroup associated to the system is exponentially stable if and only if χ 0 = 0.

TL;DR: In this article, a reaction diffusion model with logistic type growth, nonlocal delay effect and Dirichlet boundary condition is considered, and combined effect of the time delay and nonlocal spatial dispersal provides a more realistic way of modeling the complex spatiotemporal behavior.

TL;DR: In this paper, the authors considered the Fisher-KPP problem with a free boundary governed by a one-phase Stefan condition, and established the existence and uniqueness of the weak solution, and through suitable comparison arguments, extended some of the results obtained earlier in Du and Lin (2010) [11] and Du and Guo (2011) to this general case.

TL;DR: In this article, the existence and regularity of weak solution for 2D liquid crystal flows with large initial velocity was proved by using the Littlewood-Paley analysis, and the uniqueness of the weak solution was also proved.

TL;DR: In this article, the authors studied strong solutions of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a domain Ω ⊂ R 3 and proved the local existence of a unique strong solution provided that the initial data ρ 0, u 0, d 0 are sufficiently regular and satisfy a natural compatibility condition.

TL;DR: In this article, the authors established the time decay rates of the solution to the Cauchy problem for the compressible Navier-Stokes-Poisson system via a refined pure energy method.

TL;DR: In this paper, a theory of delta shock waves with Dirac delta functions developing in both state variables for a class of nonstrictly hyperbolic systems of conservation laws is established.

TL;DR: In this paper, the Liouville conjecture for a > 0 in dimension N = 3 was shown to be true in the case of bounded solutions, where p p S (a) is the Hardy-Sobolev exponent, given by (n + 2 + 2 a ) / (n − 2 ).

TL;DR: In this article, the spreading speeds and traveling wave solutions of a nonlocal dispersal equation with degenerate monostable nonlinearity were studied. And the authors proved that the critical minimal wave speed coincides with the asymptotic speed of spread.

TL;DR: In this article, the authors study measure functional differential equations and clarify their relation to generalized ordinary differential equations, and show that functional dynamic equations on time scales represent a special case of measure functional DDEs.

TL;DR: In this article, the existence of ground state solutions for the Schrodinger-Poisson system (SP) under certain assumptions on the linear and nonlinear terms was proved. But the results were not extended to the general case.

TL;DR: In this article, the authors prove the global well-posedness of the 3D micropolar fluid system in critical Besov spaces by making a suitable transformation of the solutions and using the Fourier localization method, especially combined with a new L p estimate for the Green matrix to the linear system of the transformed equation.

TL;DR: In this paper, the Cauchy problem for the integrable Novikov equation is shown to be locally well-posed in the Besov space with 1 max{1 + 1 + 1/p, 3/2} for all t is an element of [0, T] and for all u(t) is a vertices.

TL;DR: In this paper, the validity and failure of Liouville theorems and Harnack inequalities for parabolic and elliptic operators with low regularity coefficients were investigated and the existence of a modulus of continuity for solutions to the elliptic problem in two dimensions, depending on the non-scale-invariant norm of the solution.

TL;DR: In this article, a well-posedness theory of measure valued solutions to balance laws is presented, which allows to separate the differential terms from the integral ones, leading to a significant simplification of the proofs.

TL;DR: In this article, the spatial and temporal regularity of the solution process of a stochastic partial differential equation (SPDE) of evolutionary type with nonlinear multiplicative trace class noise is analyzed.

TL;DR: In this paper, the authors established new Holder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions method.

TL;DR: In this article, the authors extend the results of Diekmann et al. to the case of infinite delay and prove linearized stability for nonlinear renewal equations, delay-differential equations and coupled systems of these two types of equations.

TL;DR: In this paper, successful couplings for degenerate diffusion processes, explicit derivative formula and Harnack type inequalities are presented for solutions to a class of degenerate Fokker-Planck equations on R m × R d.