Wave fronts in a bistable reaction-diffusion system with density-dependent diffusivity

We obtain wave-front solutions for a one-dimensional bistable reaction-diffusion model with density-dependent diffusivity. These solutions — which are expected to stand for the asymptotic behaviour of a wide class of initial conditions — should describe the evolution of the walls of constant density domains, spontaneously formed in this system. The piecewise linearized form of the reaction terms and of the diffusivity makes it possible to obtain analytical results for a situation of interest in many real applications — namely, a diffusivity that changes abruptly at a critical value of the density. We pay particular attention to the dependence of the wave-front velocity on the relevant parameters, and are able to outline some physical arguments that explain its features.