Related papers: Front propagation for reaction-diffusion equations…
We study the question of periodic homogenization of a variably scaled reaction-diffusion problem with non-linear drift posed for a domain crossed by a flat composite thin layer. The structure of the non-linearity in the drift was obtained…
In this note, we demonstrated for the first time that one can derive an expression for the effective diffusion coefficient, equal to the Lifson-Jackson formula, using a subsequent homogenization of the 1D reaction-diffusion-advection…
We consider the propagation of a flame front in a solid periodic medium. The model is governed by a free boundary system in which the front's velocity depends on the temperature via a kinetic rate which may degenerate. We show the existence…
We study a Fisher-KPP equation with spatially periodic diffusion and reaction terms. We identify a class of periodic media for which the equation admits an explicit, closed-form solution. Through a nonlinear change of variables, the problem…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
We obtain a criterion for pulsating front speed-up by general periodic incompressible flows in two dimensions and in the presence of KPP nonlinearities. We achieve this by showing that the ratio of the minimal front speed and the effective…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
This paper is concerned with the existence of transition fronts for a one-dimensional twopatch model with KPP reaction terms. Density and flux conditions are imposed at the interface between the two patches. We first construct a pair of…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
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…
We consider front propagation in a reactive Boussinesq system in an infinite vertical strip. We establish nonlinear stability of planar fronts for narrow domains when the Rayleigh number is not too large. Planar fronts are shown to be…
We report on recent progress in the study of nonlinear diffusion equations involving nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous medium equation, $\partial_t u +(-\Delta)^{s}(u^m)=0$, and some…
We investigate in this paper propagation phenomena for the heterogeneous reaction-diffusion equation $\partial_t u -\Delta u = f(t,u)$, $x\in R^N$, $t\in\R$, where f=f(t,u) is a KPP monostable nonlinearity which depends in a general way on…
We consider a monostable time-delayed reaction-diffusion equation arising from population dynamics models. We let a small parameter tend to zero and investigate the behavior of the solutions. We construct accurate lower barriers --- by…
We investigate the behaviour of solutions of a fractional semilinear partial differential equation that models the evolution of an interface in a random medium. We show a pinning result and apply it to the related homogenizing process.
The evolution of the interface propagation in a slowly rotating half-filled horizontal cylinder is studied using MRI. Initially, the cylinder contains two axially segregated bands of small and large particles with a sharp interface. The…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…
A new type of boundary dynamics is proposed to describe the interface that sweeps space to collect distributed material. Based upon geometrical consideration on a simple physical process representing a certain experiment, the dynamics is…