Reaction-diffusion processes with nonlinear diffusion

Abstract

We study reaction-diffusion processes with concentration-dependent diffusivity. First, the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes is determined. We then consider two natural inhomogeneous realizations. The two-species annihilation process is investigated in the situation when the reactants are initially separated, namely each species occupies a half space. In particular, we establish the growth law of the width of the reaction zone. The single-species annihilation process is studied in the situation when the spatially localized source drives the system toward the nonequilibrium steady state. Finally, we investigate a dissolution process with a localized source of diffusing atoms which react with the initially present immobile atoms forming immobile molecules.