论文标题
退化反应扩散系统的间接扩散效应
Indirect diffusion effect in degenerate reaction-diffusion systems
论文作者
论文摘要
在这项工作中，我们研究了典型的反应系统的全球适应性和较大的时间行为 - 扩散系统，其中包括退化的扩散，其非线性是由化学反应引起的。我们表明，存在{\ it间接扩散效应}，即对非扩散物种的有效扩散，这是由于从扩散物种中扩散和物种之间的可逆反应而产生的。通过应用熵方法，我们表明该解决方案将指数成倍收敛到平衡，并提供明确的收敛速率和相关常数。
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.
