Convergence to equilibrium for a degenerate three species reaction-diffusion system

TL;DR

This paper investigates the long-term behavior of a degenerate three-species reaction-diffusion system, proving convergence to equilibrium with explicit decay constants when one diffusion coefficient vanishes.

Contribution

It provides the first analysis of convergence to equilibrium for a degenerate three-species reaction-diffusion system with explicit decay estimates.

Findings

Proved convergence to equilibrium in degenerate cases

Derived explicit decay constants for solutions

Analyzed systems with one zero diffusion coefficient

Abstract

In this work, we study a $3\times 3$ triangular reaction-diffusion system. Our main objective is to understand the long time behaviour of solutions to this reaction-diffusion system when there are degeneracies. More precisely, we treat cases when one of the diffusion coefficients vanishes while the other two diffusion coefficients stay positive. We prove convergence to equilibrium type results. In all our results, the constants appearing in the decay estimates are explicit.