Effective transmission conditions for reaction–diffusion processes in domains separated by thin channels. Issue 6 (13th April 2022)

• Record Type: Journal Article
• Authors: Bhattacharya, Apratim; Gahn, Markus; Neuss-Radu, Maria
• Is Part Of: Applicable analysis. Volume 101:Issue 6(2022)
• Page Start: 1896
• Page End: 1910
• Publication Date: 2022-04-13
• Subjects: Array of channels -- homogenization -- two-scale convergence -- reaction–diffusion equation -- effective transmission conditions; 35B27 -- 35K57 -- 35Q92; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1789599
• Languages: English
• ISSNs: 0003-6811

Abstract

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.