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 cl ass 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 diffusivit y makes it possible to obtain analytical results for a situation of in terest in many real applications - namely, a diffusivity that changes abruptly at a critical value of the density. We pay particular attenti on to the dependence of the wave-front velocity on the relevant parame ters, and are able to outline some physical arguments that explain its features.