Showing papers in "Journal of Differential Equations in 2017"

TL;DR: In this paper, the Fokas method is employed in order to study initial-boundary value problems of the general coupled nonlinear Schrodinger equation formulated on the finite interval with 3 × 3 Lax pairs.

TL;DR: In this article, the global boundedness and stability of the predator-prey system with prey-taxis in a two-dimensional bounded domain with Neumann boundary conditions was proved.

TL;DR: In this article, the authors studied the dynamics of a SIS epidemic model of reaction diffusion-advection type and found that the persistence of infected and susceptible populations and the global stability of the disease free equilibrium are established when the basic reproduction number is greater than or less than or equal to one, respectively.

TL;DR: In this article, the semiclassical limit for the singularly perturbed Choquard equation with constant coefficients was studied and the existence and multiplicity of semi-classical solutions were established by variational methods.

TL;DR: In this paper, the authors performed qualitative analysis on an SIS epidemic reaction-diffusion system with a linear source in spatially heterogeneous environment and derived uniform bounds of solutions, based on which, the threshold dynamics in terms of the basic reproduction number is established and the global stability of the unique endemic equilibrium is discussed when spatial environment is homogeneous.

TL;DR: In this article, a Hopf lemma and a strong minimum principle for weak supersolutions of ( − Δ p ) s u = c ( x ) | u | p − 2 u ǫ in Ǫ inǫ whereǫ is an open set of R N, s ∈ ( 0, 1 ), p ∈( 1, + ∞ ), c ∈ C ( Ω ‾ ), and ( ∈ cǫ ) is the fractional p-Laplacian.

TL;DR: In this paper, a complicated system obtained by mixing a nonlinear evolutionary partial differential equation and a mixed variational inequality in infinite dimensional Banach spaces in the case where the set of constraints is not necessarily bounded and the problem is driven by nonlocal boundary conditions was introduced.

TL;DR: In this article, the authors studied the threshold dynamics and ergodicity of a stochastic SIRS epidemic model with the disease transmission rate driven by a semi-Markov process.

TL;DR: In this paper, the blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent, which is closely related to the Strauss exponent, the critical number for non-damped semi-inverse wave equations.

TL;DR: In this article, sufficient conditions for the coexistence and exclusion of a stochastic competitive Lotka-Volterra model are derived, and convergence in distribution of positive solutions of the model is also established.

TL;DR: In this paper, a version of horizontal weighted Hardy-Rellich type and Caffarelli-Kohn-Nirenberg type inequalities on stratified groups and their consequences are studied.

TL;DR: In this article, the authors studied the global (in time) regularity and large time behavior of solutions to the 2D micropolar equations with only angular viscosity dissipation.

TL;DR: In this article, the authors studied the asymptotic behavior of non-autonomous gradient-like inertial dynamics with a time-dependent viscosity coefficient, and obtained convergence rates for the values, and convergence results of the trajectories under general conditions on γ ( ⋅ ).

TL;DR: In this paper, the authors studied the Cauchy problem for a nonlocal heat equation, which is of fractional order both in space and time, and proved four main theorems: (i) a representation formula for classical solutions, (ii) a quantitative decay rate at which the solution tends to the fundamental solution, (iii) optimal L 2 -decay of mild solutions in all dimensions, (iv) L 2 −decays of weak solutions via energy methods.

TL;DR: In this paper, the existence of locally bounded global solutions to the chemotaxis system was shown for smooth bounded domains, provided that m > 1 + N 4 + √ n 4.

TL;DR: In this article, the authors considered the nonlocal Cahn-Hilliard equation with singular potential and constant mobility, and established the validity of the strict separation property in dimension two.

TL;DR: In this paper, the problem of periodic orbit bifurcations for high-dimensional piecewise smooth systems was studied and a formula for the first order Melnikov vector function was developed, which can be used to study the number of periodic orbits that can be separated from the periodic orbits.

TL;DR: In this article, the authors consider a class of nonlocal balance laws as initial value problems on a finite time horizon and show existence and uniqueness of the corresponding weak solutions, resulting in a fixed-point problem in the nonlocal term.

TL;DR: In this paper, it was shown that if n ≤ 5, then for all suitably regular initial data an associated no-flux initial-boundary value problem admits a global weak solution, which is the first result on global existence in a system of the form (⋆) in a spatially three-dimensional setting when arbitrarily large initial data and parameters are involved.

TL;DR: In this paper, the authors studied the 3D focusing inhomogeneous nonlinear Schrodinger equation and showed that if the radial initial data u 0 belongs to H 1 ( R 3 ) and satisfies E ( u 0 ) s c m c m m c 1 − s c E ( Q ) sc m c M 1 − m c ( q ) 1 − 1 + b ) / 2, then the corresponding solution is global and scatters in H 1(R 3 ).

TL;DR: In this paper, the authors considered the parabolic-elliptic semilinear Keller-Segel model on RNRN and proved the local existence and uniqueness of classical solutions.

TL;DR: In this paper, the two-species chemotaxis-Navier-Stokes system with Lotka-Volterra competitive kinetics was studied and the results for global existence, boundedness and stabilization of solutions were given.

TL;DR: In this article, the authors give a simple proof of the existence of global-in-time smooth solutions for the convective Brinkman-Forchheimer equations (called the tamed Navier-Stokes equations) ∂ t u − μ Δ u + ( u ⋅ ∇ ) u + ∇ p + α u + β | u | r − 1 u = 0 on a 3D periodic domain.

TL;DR: In this article, the existence/nonexistence of travelling waves and the propagation properties of the Cauchy problem were investigated and the exact separation between existence and nonexistence of traveling waves was shown.

TL;DR: In this paper, it was shown that for all reasonable initial data solutions of the Keller-Segel system, in the case n = 4, a Lyapunov functional can be constructed and the constant (8 π ) 2 / χ is deduced from the critical constant in the Adams type inequality.

TL;DR: In this paper, the existence of solutions of the L p Monge-Ampere equation for arbitrary measures is proved for the case where 0 p 1, and the solution is in general not unique.

TL;DR: In this article, the authors employ the concentration compactness techniques to prove existence and stability results of standing waves for nonlinear fractional Schrodinger-Choquard equation i ∂ t Ψ + ( − Δ ) α Ψ = a, λ are nonnegative satisfying a + λ ≠ 0.

TL;DR: In this article, sufficient conditions for constructing a random exponential attractor for a continuous cocycle on a separable Banach space and weighted spaces of infinite sequences were established and applied to study the existence of non-autonomous first order dissipative lattice dynamical systems with multiplicative white noise.

TL;DR: In this article, the Keller-Segel-Navier-Stokes system was considered for the initial boundary problem with κ ≠ 0, and it was shown that the problem admits at least one weak solution if α ≥ 3 7.

TL;DR: In this paper, a coupled chemotaxis-Navier-stokes system in the two-dimensional setting was considered and the global existence of weak solutions and classical solutions for both the Cauchy problem and the initial-boundary value problem supplemented with some initial data.