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arXiv · 2003.11946

Effective transmission conditions for reaction-diffusion processes in domains separated by thin channels

Apratim Bhattacharya·Markus Gahn·Maria Neuss-Radu
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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 $\epsilon$, and the equation inside the layer depends on the parameter $\epsilon$ 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 $\epsilon \to 0 $, when the channel-domain is replaced by an interface between the two bulk-domains.

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Apratim Bhattacharya, Markus Gahn, Maria Neuss-Radu. 2020-03-26. Effective transmission conditions for reaction-diffusion processes in domains separated by thin channels. https://doi.org/10.1080/00036811.2020.1789599

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