Showing papers in "Journal of Differential Equations in 2019"

TL;DR: In this article, the authors investigated the long-time asymptotics of the focusing Kundu-Eckhaus equation with nonzero boundary conditions at infinity by the nonlinear steepest descent method of Deift and Zhou.

TL;DR: In this article, the authors prove norm inflation and hence illposedness for a class of shallow water wave equations, such as the Camassa-Holm equation, Degasperis-Procesi equation and Novikov equation etc., in the critical Sobolev space H 3 / 2 and even in the Besov space B p, r 1 + 1 / p for p ∈ [ 1, ∞ ], r ∈ ( 1, ∞ ).

TL;DR: In this article, it was shown that the solution of the non-local double phase problem is Holder continuous, which is the first regularity result for nonlocal double-phase problems.

TL;DR: In this paper, the spatiotemporal dynamics of the single population model with memory-based diffusion and non-local reaction were investigated and the impact of the averaged memory period on stability and bifurcation was investigated.

TL;DR: In this article, the authors prove C 1, ν -regularity for local minimizers of the multi-phase energy: w ↦ ∫ ∫ Ω | D w | p + a (x )| q + b (x)| D w| s d x, under sharp assumptions relating the couples ( p, q ) and ( p, s ) to the Holder exponents of the modulating coefficients a ( ⋅ ) and b ( ⊅ ), respectively.

TL;DR: A susceptible-infectious-recovered (SIRS) epidemic model with a generalized nonmonotone and saturated incidence rate is studied.

TL;DR: In this article, a susceptible-exposed-infected-recovered-susceptible (SEIRS) reaction-diffusion model is proposed, where the disease transmission and recovery rates can be spatially heterogeneous.

TL;DR: In this paper, a new Cahn-Hilliard-Brinkman model for tumour growth allowing for chemotaxis is introduced and mathematically analyzed, and the existence of global-in-time weak solutions is shown in a very general setting.

TL;DR: In this paper, a framework of test function methods was proposed to derive sharp upper bounds for the lifespan of solutions to nonlinear wave equations and their systems, including time-derivatives of unknown functions and weakly coupled systems.

TL;DR: In this paper, the minimal-speed determinacy of traveling wave fronts of a two-species competition model of diffusive Lotka-Volterra type is investigated, and the upper-lower solution technique on the cooperative system to study the traveling waves as well as its minimal speed selection mechanisms: linear or nonlinear.

TL;DR: In this article, a blow-up result for solutions to a semi-linear wave equation with scale-invariant dissipation and mass and power non-linearity was obtained.

TL;DR: In this paper, it was shown that for any sufficiently regular nonnegative initial data there exists at least one global boundedness solution for system (K S F ), which in view of the known results for the fluid-free system mentioned below is an optimal restriction on m.

TL;DR: In this paper, the exterior Dirichlet problem for the heterogeneous Helmholtz equation is considered and new a priori bounds on the solution under conditions on A, n, and the domain that ensure nontrapping of rays are proved.

TL;DR: In this article, the authors consider the problem of the long time dynamics for a diffuse interface model for tumor growth and prove that the corresponding initial-boundary value problem generates a dissipative dynamical system that admits the global attractor in a proper phase space.

TL;DR: In this article, Bismut type formulas are established for the Lions derivative of P t f (μ) : = E f ( X t μ ), where t > 0, f is a bounded measurable function, and X tμ solves a distribution dependent SDE with initial distribution μ.

TL;DR: In this article, the authors studied the asymptotic behavior of the solutions of the fractional reaction-diffusion equations with polynomial drift terms of arbitrary order driven by locally Lipschitz nonlinear diffusion terms defined on R n.

TL;DR: In this paper, minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions are studied and stronger conditions than continuity leading to input-to-state stability with respect to Orlicz spaces are investigated.

TL;DR: In this paper, a competitive system with nonlocal dispersals in a 1-dimensional environment that is worsening with a constant speed, reflected by two shifting growth functions, is considered and the spatial-temporal dynamics of the model system is analyzed.

TL;DR: In this article, the authors investigated the large time behavior of strong solutions to a chemotaxis-fluids system in an unbounded domain with mixed boundary conditions and derived the global existence of strong solution around the equilibrium state ( 0, c satn, 0 ) with the help of the continuity arguments.

TL;DR: In this paper, a nonlinear Dirichlet problem driven by the p-Laplace operator and with a right-hand side which has a singular term and a parametric superlinear perturbation is considered and a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter λ > 0 varies.

TL;DR: In this article, the existence part of the L p dual Minkowski problem was solved for p > 1 and q > 0, and also the regularity of the solution was discussed.

TL;DR: In this paper, the authors studied the optimal control of discontinuous differential inclusions of the normal cone type governed by a generalized version of the Moreau sweeping process with control functions acting in both nonconvex moving sets and additive perturbations.

TL;DR: In this article, the existence, uniqueness and continuous dependence of mild solutions to stochastic delay evolution equations with a Caputo fractional derivative were proved, and the existence of a global forward attracting set in the mean-square topology was established.

TL;DR: In this paper, it was shown that solutions of stochastic nonlinear Schrodinger (NLS) equations can be approximated by solutions of coupled splitting systems, and a new kind of fully discrete splitting schemes were proposed which possess algebraic strong convergence rates for nonlinear NLS equations.

TL;DR: In this paper, a Lotka-Volterra competition-diffusion-advection system was used to reveal the combined effect of movement and spatial variations on the outcome of competition.

TL;DR: In this article, the local boundedness of subsolutions of non-local, possibly degenerate, parabolic integro-differential equations of the form ∂ t u (x, y, t ) + P.V.

TL;DR: In this paper, it was shown that if the positive smooth function D decays at most algebraically with respect to u, then for any smooth nonnegative and bounded S satisfying a mild assumption especially satisfied when S ≡ S ( u ) with S ( 0 ) = 0, (⋆) possesses a globally defined classical solution.

TL;DR: In this article, the critical case p = p 0 (n) of Strauss' conjecture was verified, where n ≥ 2 and the perturbations of the Laplace operator decay exponentially fast at infinity.

TL;DR: In this paper, a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition was studied, where the spatial movement of individuals is described by a non-local (convolution) diffusion operator, the transmission rate and recovery rate are spatially heterogeneous, and the total population number is constant.

TL;DR: In this article, the stability switching properties of a general transcendental equation were studied for a model with two discrete time delays and delay dependent parameters that dependent only on one of the time delays.