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

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 γ∈[−1,1), which describes the size of the diffusion in the layer. We derive effective models for the limit ϵ→0, when the channel-domain is replaced by an interface between the two bulk-domains.

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