Stochastic homogenization on irregularly perforated domains

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Date
2021
Volume
2880
Issue
Journal
Series Titel
WIAS Preprints
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract

We study stochastic homogenization of a quasilinear parabolic PDE with nonlinear microscopic Robin conditions on a perforated domain. The focus of our work lies on the underlying geometry that does not allow standard homogenization techniques to be applied directly. Instead we prove homogenization on a regularized geometry and demonstrate afterwards that the form of the homogenized equation is independent from the regularization. Then we pass to the regularization limit to obtain the anticipated limit equation. Furthermore, we show that Boolean models of Poisson point processes are covered by our approach.

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Citation
Heida, M., Jahnel, B., & Vu, A. D. (2021). Stochastic homogenization on irregularly perforated domains (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2880
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