Related papers: Blocking and invasion for reaction-diffusion equat…
This paper is concerned with the existence of pulsating travelling fronts for a KPP reaction-diffusion equation posed in a multi-dimensional periodic medium. We provide an alternative proof of the classic existence result. Our proof relies…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…
Mineral replacement reactions under advective flow often suffer from severe spatial inefficiency: dissolution causes the flow to self-focus into a few dominant wormholes that bypass the surrounding matrix, leaving most of the rock…
Properties of reaction zones resulting from A+B -> C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic…
We consider in this paper a diffusion-convection reaction equation in one space dimension. The main assumptions are about the reaction term, which is monostable, and the diffusivity, which changes sign once or twice; then, we deal with a…
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…
The interaction of a Zeldovich reaction-diffusion front with a localized defect is studied numerically and analytically. For the analysis, we start from conservation laws and develop simple collective variable ordinary differential…
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…
Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid re-arrangements of the medium constantly change the effective diffusivity felt…
We present a unified approach to characterising fast-reaction limits of systems of either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential equation, on unbounded domains, motivated by models…
In this article we study the asymptotic behaviour of the solution of the three species chemical reaction-diffusion model with non-homogeneous Neumann boundary condition in a perforated domain. We investigate how the mass inflow at the…
We study invasion fronts and spreading speeds in two component reaction-diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the existence of a bifurcation to locked fronts where both…
We consider reaction-diffusion equations of porous medium type, with different kind of reaction terms, and nonnegative bounded initial data. For all the reaction terms under consideration there are initial data for which the solution…
We devote this paper to the issue of existence of pulsating travelling front solutions for spatially periodic heterogeneous reaction-diffusion equations in arbitrary dimension, in both bistable and more general multistable frameworks. In…
We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities (including multistable ones) and study the asymptotic behavior of solutions with Heaviside type initial data. Our analysis…
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…
The present paper is devoted to the study of transition fronts in nonlocal reaction-diffusion equations with time heterogeneous nonlinearity of ignition type. It is proven that such an equation admits space monotone transition fronts with…
In this study, we investigate the dynamics of moving fronts in three-dimensional spaces, which form as a result of in-situ combustion during oil production. This phenomenon is also observed in other contexts, such as various autowave models…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
This paper deals with the homogenization of the $p$-Laplacian reaction-diffusion problems in a domain containing periodically distributed holes of size $\varepsilon$, with a dynamical boundary condition of pure-reactive type. We generalize…