Exponential convergence to equilibrium for nonlinear reaction-diffusion systems arising in reversible chemistry

Abstract

We consider a prototypical nonlinear reaction-diffusion system arising in reversible chemistry. Based on recent existence results of global weak and classical solutions derived from entropy-decay related a-priori estimates and duality methods, we prove exponential convergence of these solutions towards equilibrium with explicit rates in all space dimensions. The key step of the proof establishes an entropy entropy-dissipation estimate, which relies only on natural a-priori estimates provided by mass-conservation laws and the decay of an entropy functional.