Reaction-Diffusion Processes with Nonlinear Diffusion

Abstract

We study reaction-diffusion processes with concentration-dependent diffusivity. First, we determine the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes. 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 determine 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 non-equilibrium steady state. Finally we investigate a dissolution process with a localized source of diffusing atoms which react with initially present immobile atoms forming immobile molecules.

Figure and references added, final version

References in corpus (5)

• Generalized Diffusion
• A microscopic approach to nonlinear Reaction-Diffusion: the case of morphogen gradient formation
• Compact Waves in Microscopic Nonlinear Diffusion
• Reaction-Diffusion Process Driven by a Localized Source: First Passage Properties
• Width of reaction zones in A + B -> C type reaction-diffusion processes: Effects of an electric current

Cited by in corpus (3)

• Aggregation in non-uniform systems with advection and localized source
• Aggregation Driven by a Localized Source
• Assortative Exchange Processes