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

In this work, we study a reaction-diffusion system for three species. The nonlinearity in the system comes from an underlying chemical reaction. 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.