  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.
