Related papers: Blocking of 2D bistable reaction-diffusion fronts …
In this paper we consider a bistable reaction-diffusion equation in unbounded domains and we investigate the existence of propagation phenomena, possibly partial, in some direction or, on the contrary, of blocking phenomena. We start by…
We study the persistence and propagation (or blocking) phenomena for a species in periodically hostile environments. The problem is described by a reaction-diffusion equation with zero Dirichlet boundary condition. We first derive the…
We consider a bistable reaction-diffusion equation $u_t=\Delta u +f(u)$ on $\mathbb{R}^N$ in the presence of an obstacle $K$, which is a wall of infinite span with many holes. More precisely, $K$ is a closed subset of $\mathbb{R}^N$ with…
We investigate the large time behavior of solutions of reaction-diffusion equations with general reaction terms in periodic media. We first derive some conditions which guarantee that solutions with compactly supported initial data invade…
We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially non-homogeneous. This equation has been used to model wave propagation in various biological systems. Extending previous…
This paper is concerned with the interaction between a planar traveling front and a compact obstacle for monotone bistable reaction-diffusion systems in exterior domains. By constructing appropriate sub- and supersolutions, we first…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
We study analytically and numerically a bistable reaction-diffusion equation on an arbitrary finite network. We prove that stable fixed points (multi-fronts) exist for any configuration as long as the diffusion is small. We also study fold…
We consider reaction-diffusion fronts in spatially periodic bistable media with large periods. Whereas the homogenization regime associated with small periods had been well studied for bistable or Fisher-KPP reactions and, in the latter…
Recent theoretical and experimental work has demonstrated the existence of one-sided, invariant barriers to the propagation of reaction-diffusion fronts in quasi-two-dimensional periodically-driven fluid flows. These barriers were called…
In this paper, curved fronts are constructed for spatially periodic bistable reaction-diffusion equations under the a priori assumption that there exist pulsating fronts in every direction. Some sufficient and some necessary conditions of…
We consider a class of singularly perturbed 2-component reaction-diffusion equations which admit bistable traveling front solutions, manifesting as sharp, slow-fast-slow, interfaces between stable homogeneous rest states. In many example…
We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal…
Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction…
This paper is concerned with propagation phenomena for the solutions of the Cauchy problem associated with a two-patch one-dimensional reaction-diffusion model. It is assumed that each patch has a relatively well-defined structure which is…
Propagation of traveling fronts in three-dimensional reaction-diffusion media with spatially modulated cross-section is studied using the Schl\"ogl model as a representative example. Applying appropriate perturbation techniques leads first…
We consider bistable reaction-diffusion equations in funnel-shaped domains of R N made up of straight parts and conical parts with positive opening angles. We study the large time dynamics of entire solutions emanating from a planar front…
Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…
In this paper we derive quantitative conditions under which a compactly supported drift term depending on the direction of propagation blocks a traveling wave solution or lets it pass almost unchanged. We give explicit conditions on the…