SIAM Journal on Mathematical Analysis, Volume 52, Issue 5, Page 4314-4361, January 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.

中文翻译：

---

简并反应扩散系统中的间接扩散效应

SIAM数学分析杂志，第52卷，第5期，第4314-4361页，2020
年1月。在这项工作中，我们研究了典型的反应扩散系统的全局适定性和长时间行为，该系统包括退化扩散和其非线性现象来自化学反应。我们表明存在间接扩散效应，即非扩散物质的有效扩散是由于扩散物质的扩散与物质之间可逆反应的结合而引起的。通过对此类退化的反应扩散系统进行新的估算，我们证明了通过应用熵方法，该解决方案以指数形式收敛到平衡，并提供了明确的收敛速度和相关常数。