Related papers: Homogenization for Time-periodic KPP Reactions
In this paper, we investigate the asymptotic dynamics of Fisher-KPP equations with nonlocal dispersal operator and nonlocal reaction term in time periodic and space heterogeneous media. We first show the global existence and boundedness of…
We study the uniqueness of steady states of strong-KPP reaction--diffusion equations in general domains under various boundary conditions. We show that positive bounded steady states are unique provided the domain satisfies a certain…
This paper is concerned with some nonlinear propagation phenomena for reaction-advection-diffusion equations with Kolmogrov-Petrovsky-Piskunov (KPP) type nonlinearities in general periodic domains or in infinite cylinders with oscillating…
In this paper, we study the stochastic-periodic homogenization of Non-stationary Navier-Stokes Type Equations on anisotropic heterogeneous media. More precisely, we are interested in the stochastic-periodic homogenization of its variational…
We use a new method in the study of Fisher-KPP reaction-diffusion equations to prove existence of transition fronts for inhomogeneous KPP-type non-linearities in one spatial dimension. We also obtain new estimates on entire solutions of…
This paper concerns the nonautonomous reaction-diffusion equation \[ u_t=u_{xx}+ug(t,x-ct,u), \quad t>0,x\in\mathbb{R}, \] where $c\in\mathbb{R}$ is the shifting speed, and the time periodic nonlinearity $ug(t,\xi,u)$ is asymptotically of…
In this paper, we study the existence and stability of random transition waves for time heterogeneous Fisher-KPP Equations with nonlocal diffusion. More specifically, we consider general time heterogeneities both for the nonlocal diffusion…
We take interest in a reaction-diffusion system which has been recently proposed [11] as a model for the effect of a road on propagation phenomena arising in epidemiology and ecology. This system consists in coupling a classical Fisher-KPP…
The notion of traveling wave, which typically refers to some particular spatio-temporal con- nections between two stationary states (typically, entire solutions keeping the same profile's shape through time), is essential in the…
We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global in time solutions while…
Homogenization of a stochastic nonlinear reaction-diffusion equation with a large non- linear term is considered. Under a general Besicovitch almost periodicity assumption on the coefficients of the equation we prove that the sequence of…
We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may oscillate on the microscopic scale and is…
In this paper we provide a rate of convergence for periodic homogenization of Hamilton-Jacobi-Bellman equations with nonlocal diffusion. The result is based on the regularity of the associated effective problem, where the convexity plays a…
We present a simple new proof for the stochastic homogenization of quasiconvex (level-set convex) Hamilton-Jacobi equations set in stationary ergodic environments. Our approach, which is new even in the convex case, yields more information…
This paper is devoted to the analysis of the large-time behavior of solutions of one-dimensional Fisher-KPP reaction-diffusion equations. The initial conditions are assumed to be globally front-like and to decay at infinity towards the…
We prove homogenization for a nondegenerate viscous Hamilton-Jacobi equation in dimension one in stationary ergodic environments with a superlinear (nonconvex) Hamiltonian of fairly general type. The version of the paper herein posted is…
We study analytically and numerically a model describing front propagation of a KPP reaction in a fluid flow. The model consists of coupled one-dimensional reaction-diffusion equations with different drift coefficients. The main rigorous…
This paper is devoted to propagation phenomena for a reaction-diffusion-advection equation in a one-dimensional heterogeneous environment, where heterogeneity is reflected by the nonlinearity term -- being KPP type on $(-\infty, -L]$ and…
This paper is devoted to the homogenization of Shr\"odinger type equations with periodically oscillating coefficients of the diffusion term, and a rapidly oscillating periodic time-dependent potential. One convergence theorem is proved and…
This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions of some reaction-diffusion equations in R N in any space dimension N. The solutions are assumed to be localized in the past. Under certain…