Reaction-Diffusion Processes with Nonlinear Diffusion

TL;DR

This paper investigates reaction-diffusion processes with nonlinear, concentration-dependent diffusivity, analyzing decay behaviors, reaction zone growth, and steady states in various inhomogeneous scenarios.

Contribution

It introduces new analyses of reaction-diffusion systems with nonlinear diffusion, including decay laws, reaction zone dynamics, and steady-state behaviors in inhomogeneous settings.

Findings

Decay laws for concentration in single and two-species processes

Growth law of the reaction zone when reactants are initially separated

Steady-state behavior in localized source-driven systems

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.