Indirect diffusion effect in degenerate reaction-diffusion systems

TL;DR

This paper investigates a reaction-diffusion system with degenerate diffusion, demonstrating an indirect diffusion effect that leads to exponential convergence to equilibrium through entropy methods.

Contribution

It introduces the concept of indirect diffusion effect in degenerate systems and derives explicit convergence rates using new estimates and entropy techniques.

Findings

Existence of an indirect diffusion effect in degenerate systems

Exponential convergence to equilibrium proven

Explicit rates and constants provided

Abstract

In this work we study global well-posedness and large time behaviour for a typical reaction--diffusion system, which include degenerate diffusion, and whose non-linearities arise from chemical reactions. We show that there is an {\it indirect diffusion effect}, i.e. an effective diffusion for the non-diffusive species which is incurred by a combination of diffusion from diffusive species and reversible reactions between the species. Deriving new estimates for such degenerate reaction-diffusion system, we show, by applying the entropy method, that the solution converges exponentially to equilibrium, and provide explicit convergence rates and associated constants.