Homogenization of a reaction-diffusion-advection problem in an evolving micro-domain and including nonlinear boundary conditions
Abstract
We consider a reaction-diffusion-advection problem in a perforated medium, with nonlinear reactions in the bulk and at the microscopic boundary, and low 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.
Keywords
Cite
@article{arxiv.2011.12915,
title = {Homogenization of a reaction-diffusion-advection problem in an evolving micro-domain and including nonlinear boundary conditions},
author = {Markus Gahn and Maria Neuss-Radu and Iulio Sorin Pop},
journal= {arXiv preprint arXiv:2011.12915},
year = {2021}
}