Indirect Diffusion Effect in Degenerate Reaction-Diffusion Systems
Amit Einav, J. D. Morgan, Bao Quoc Tang · SIAM Journal on Mathematical Analysis · 2020
In this work we study global well-posedness and large time behavior for a typical reaction-diffusion system, which include degenerate diffusion, and whose nonlinearities arise from chemical reactions. We show that there is an indirect diffusion effect, i.e., an effective diffusion for the nondiffusive 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 systems, we show, by applying the entropy method, that the solution converges exponentially to equilibrium, and provide explicit convergence rates and associated constants.