SINGULAR LIMIT FOR REACTIVE DIFFUSIVE TRANSPORT THROUGH AN ARRAY OF THIN CHANNELS IN CASE OF CRITICAL DIFFUSIVITY

Gahn M, Neuss-Radu M (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Multiscale Modeling & Simulation Society for Industrial and Applied Mathematics

Book Volume: 19

Pages Range: 1573-1600

Journal Issue: 4

DOI: 10.1137/21M1390505

Abstract

We consider a nonlinear 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 . We consider the critical scaling of the diffusion coefficients in the channels and nonlinear Neumann boundary condition on the channels' lateral boundaries. We derive effective models in the limit \epsilon \rightarrow 0, when the channel domain is replaced by an interface \Sigma between the two bulk domains. Due to the critical size of the diffusion coefficients, we obtain jumps for the solution and its normal fluxes across \Sigma , involving the solutions of local cell problems on the reference channel in every point of the interface \Sigma .

Authors with CRIS profile

Maria Neuß Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Ruprecht-Karls-Universität Heidelberg DE Germany (DE)

How to cite

APA:

Gahn, M., & Neuss-Radu, M. (2021). SINGULAR LIMIT FOR REACTIVE DIFFUSIVE TRANSPORT THROUGH AN ARRAY OF THIN CHANNELS IN CASE OF CRITICAL DIFFUSIVITY. Multiscale Modeling & Simulation, 19(4), 1573-1600. https://doi.org/10.1137/21M1390505

MLA:

Gahn, Markus, and Maria Neuss-Radu. "SINGULAR LIMIT FOR REACTIVE DIFFUSIVE TRANSPORT THROUGH AN ARRAY OF THIN CHANNELS IN CASE OF CRITICAL DIFFUSIVITY." Multiscale Modeling & Simulation 19.4 (2021): 1573-1600.

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