Homogenization of a reaction-diffusion-advection problem in an evolving micro-domain and including nonlinear boundary conditions

Gahn M, Neuss-Radu M, Pop IS (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Journal of Differential Equations Elsevier

Book Volume: 289

Pages Range: 95-127

DOI: 10.1016/j.jde.2021.04.013

Abstract

We consider a reaction-diffusion-advection problem in a perforated medium, with nonlinear reactions in the bulk and at the microscopic boundary, and slow diffusion scaling. The microstructure changes in time; the microstructural evolution is known a priori. The aim of the paper is the rigorous derivation of a homogenized model. We use appropriately scaled function spaces, which allow us to show compactness results, especially regarding the time-derivative and we prove strong two-scale compactness results of Kolmogorov-Simon-type, which allow to pass to the limit in the nonlinear terms. The derived macroscopic model depends on the micro- and the macro-variable, and the evolution of the underlying microstructure is approximated by time- and space-dependent reference elements.

Authors with CRIS profile

Maria Neuß Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Ruprecht-Karls-Universität Heidelberg DE Germany (DE) Hasselt University / Universiteit Hasselt BE Belgium (BE)

How to cite

APA:

Gahn, M., Neuss-Radu, M., & Pop, I.S. (2021). Homogenization of a reaction-diffusion-advection problem in an evolving micro-domain and including nonlinear boundary conditions. Journal of Differential Equations, 289, 95-127. https://dx.doi.org/10.1016/j.jde.2021.04.013

MLA:

Gahn, M., Maria Neuss-Radu, and I. S. Pop. "Homogenization of a reaction-diffusion-advection problem in an evolving micro-domain and including nonlinear boundary conditions." Journal of Differential Equations 289 (2021): 95-127.

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