Effective transmission conditions for reaction–diffusion processes in domains separated by thin channels. Issue 6 (13th April 2022) - Bhattacharya, Apratim; Gahn, Markus; Neuss-Radu, Maria
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.