Showing papers in "Journal of Differential Equations in 2014"

TL;DR: In this paper, the authors considered the quasilinear fully parabolic Keller-Segel system under homogeneous Neumann boundary conditions in a bounded domain, where diffusivity D ( u ) is assumed to satisfy algebraic growth and D ( 0 ) ⩾ 0, which says that the diffusion is allowed to be not only non-degenerate but also degenerate.

TL;DR: In this article, the authors studied the nonlinear problem of Kirchhoff type with pure power nonlinearities and proved that (0.1) has a positive ground state solution by using a monotonicity trick and a new version of global compactness lemma.

TL;DR: In this article, it was shown that the unique nontrivial spatially homogeneous equilibrium given by u = v ≡ 1 μ is globally asymptotically stable in the sense that for any choice of suitably regular nonnegative initial data (u 0, v 0 ) such that u 0 ≢ 0, the above problem possesses a uniquely determined global classical solution ( u, v ) with ( u, v ) | t = 0 = ( u 0, v 0) which satisfies ∞ ∞ as t → ∞.

TL;DR: In this article, the authors considered the semilinear equation e 2 s ( − Δ ) s u + V ( x ) u − u p = 0, u > 0, u ∈ H 2 s n (R N ) where 0 s 1, 1 p N + 2 s N − 2 s, V (x ) is a sufficiently smooth potential with inf R V(x ) > 0, and e > 0 is a small number.

TL;DR: In this paper, the authors considered the delay differential equation (DDE) and the corresponding ODE for the bistable case and showed that both the DDE and ODE share three equilibria.

TL;DR: In this paper, an optimal blow-up criterion for classical solutions to the incompressible resistive Hall-magnetohydrodynamic equations is established, and two global-in-time existence results of the classical solutions for small initial data, the smallness conditions of which are given by the suitable Sobolev and the Besov norms respectively.

TL;DR: In this paper, the authors considered a predator-prey system with generalized Holling type III functional response and showed that the model exhibits subcritical Hopf and Bogdanov-Takens bifurcation simultaneously in corresponding small neighborhoods of the two degenerate equilibria.

TL;DR: In this paper, it was shown that for any sufficiently smooth initial data (u0,w0) satisfying first-order compatibility conditions, the model admits a unique global smooth solution, and a crucial ingredient in the proof is an energy-like inequality which yields boundedness of u(⋅,t) in LlogL(Ω).

TL;DR: In this paper, the authors studied the Kirchhoff type elliptic problem and proved the existence of solutions of (P) using the variational method and the concentration compactness argument for PS sequences.

TL;DR: In this article, the authors investigated the free boundary problems for the Lotka-Volterra type prey-predator model in one space dimension, and provided an estimate to show that the spreading speed (if exists) cannot be faster than the minimal speed of traveling wavefront solutions for the predator model on the whole real line without a free boundary.

TL;DR: In this paper, an indefinite Kirchhoff type equation with steep potential well is studied and the existence and non-existence of nontrivial solutions are obtained by using variational methods.

TL;DR: In this article, a quasilinear parabolic-elliptic chemotaxis system with logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain, is considered.

TL;DR: In this paper, a parametric nonlinear Robin problem driven by the p-Laplacian was considered, and it was shown that the problem has at least three nontrivial solutions, two of constant sign and the third nodal.

TL;DR: In this paper, a generalized quasilinear Choquard equation was studied, where Δ p is the p-Laplacian operator, 1 p N, V and Q are two continuous real functions on R N, 0 μ N, F ( s ) is the primate function of f ( s ), and e is a positive parameter.

TL;DR: In this paper, the authors studied the existence and uniqueness of weak solutions to (E) ( − Δ ) α u + g ( u ) = ν in a bounded regular domain Ω in R N ( N ≥ 2 ) which vanish in R n ∖ Ω, where α denotes the fractional Laplacian with α ∈ ( 0, 1 ), ν is a Radon measure and g is a nondecreasing function satisfying some extra hypotheses.

TL;DR: In this article, the authors studied standing waves for a model of nonlinear Schr\"odinger equation on a graph, where the graph is obtained by joining $N$ halflines at a vertex, i.e. it is a star graph.

TL;DR: In this article, the existence of nodal and multiple solutions of nonlinear problems involving the fractional Laplacian is studied, where the authors show that if f (x, u ) is odd in u, then there is a positive solution, a negative solution, and a nodal solution.

TL;DR: In this paper, the authors considered the Cauchy problem in R n for strongly damped wave equations and derived asymptotic profiles of these solutions with weighted L 1, 1 (R n ) data using a method introduced in [9] and/or [10].

TL;DR: In this article, an SIR model with a standard incidence rate and a nonlinear recovery rate was established to consider the impact of available resource of the public health system especially the number of hospital beds.

TL;DR: In this paper, the authors consider the case of compactly supported interactions between agents which are also non-symmetric, including for instance the so-called Krause model, and prove the convergence to a final equilibrium state composed of possibly several local consensus.

TL;DR: In this article, the authors derived L p − L q decay estimates for the difference u − v + and its time and space derivatives, where L p ⩽ q ∞, possibly not on the conjugate line, satisfying some additional condition related to σ.

TL;DR: In this paper, the authors study the population dynamics of an invasive species in heterogeneous environment which is modeled by a diffusive logistic equation with free boundary condition, and derive sufficient conditions for species spreading (resp. vanishing) in the strong and weak heterogeneous environments, respectively.

TL;DR: In this paper, the existence of entire solutions for a quasilinear equation (E λ ) in R N, depending on a real parameter λ, which involves a general variable exponent elliptic operator A in divergence form and two main nonlinearities.

TL;DR: In this paper, the authors considered the initial boundary value problem of the 3D primitive equations for oceanic and atmospheric dynamics with only horizontal diffusion in the temperature equation, and established the global well-posedness of strong solutions with H2 initial data.

TL;DR: In this paper, the existence of global C 1 piecewise weak solutions for the discrete Cucker-Smale's flocking model with a non-Lipschitz communication weight ψ ( s ) = s − α, 0 α 1.

TL;DR: In this article, the existence of positive solutions, negative solutions and sequence of high energy solutions for quasilinear Schrodinger equations with the form − Δ u + V (x ) u − Δ ( | u | 2 α ) | u| 2 α − 2 u = g ( x, u ), x ∈ R N, where 1 ⩾ α > 1 2, V ∈ C (R N, R ), g ∈ c ( R N × R, R ).

TL;DR: In this article, an approach to obtain successfully an optimal rate of uniform decay for the system energy, only under basic conditions on the memory kernels, is presented. And the same rate is also obtained (with less difficulty) for the corresponding single memory-dissipative second order evolution equations.

TL;DR: In this article, a purely variational approach to time dependent problems, yielding the existence of global parabolic minimizers, was introduced, where the evolutionary variational solutions are obtained as limits of maps depending on space and time minimizing certain convex variational functionals.

TL;DR: In this paper, the well-posedness of a class of first order Hamilton-Jacobi equations in geodesic metric spaces was established, and the result was then applied to solve a Hamilton -Jacobi equation in the Wasserstein space of probability measures, which arises from the variational formulation of a compressible Euler equation.

TL;DR: In this paper, a strongly coupled PDE-ODE system is considered to describe the influence of a slow and large vehicle on road traffic. But the model consists of a scalar conservation law accounting for the main traffic evolution, while the trajectory of the slower vehicle is given by an ODE depending on the downstream traffic density.