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We consider a system of reaction-diffusion equations describing thereversible reaction of two species $\mathcal{U}, \mathcal{V}$ forming a thirdspecies $\mathcal{W}$ and vice versa according to mass action law kinetics witharbitrary stochiometric coefficients (equal or larger than one).  Firstly, we prove existence of global classical solutions via improvedduality estimates under the assumption that one of the diffusion coefficientsof $\mathcal{U}$ or $\mathcal{V}$ is sufficiently close to the diffusioncoefficient of $\mathcal{W}$.  Secondly, we derive an entropy entropy-dissipation estimate, that is afunctional inequality, which applied to global solutions of thesereaction-diffusion system proves exponential convergence to equilibrium withexplicit rates and constants.

Exponential decay towards equilibrium and global classical solutions for nonlinear reaction-diffusion systems