ABSTRACT

We consider a reaction–diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order ε, and the equation inside the layer depends on the parameter ε and an additional parameter $\gamma \in [-1,1)$, which describes the size of the diffusion in the layer. We derive effective models for the limit $ϵ\to 0$, when the channel-domain is replaced by an interface between the two bulk-domains.

中文翻译：

---

由薄通道分隔的区域中反应扩散过程的有效传输条件

摘要

我们考虑了一个域中的反应扩散方程，该域由两个通过周期性分布在薄层内的小通道连接的块状区域组成。通道的高度和厚度为ε阶，层内的方程取决于参数ε和一个附加参数$\gamma \in [-1,1)$，它描述了层中扩散的大小。我们推导出极限的有效模型$\epsilon \to 0$，当通道域被两个体域之间的接口替换时。