WIAS Preprint No. 2880, (2021)

Stochastic homogenization on irregularly perforated domains


Authors

  • Heida, Martin
    ORCID: 0000-0002-7242-8175
  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Vu, Anh Duc
    ORCID: 0009-0005-6913-4992

2020 Mathematics Subject Classification

  • 74Q05 47J30 60K35

Keywords

  • Compensated compactness, Robin boundary condition, continuum percolation, Poisson point process

DOI

10.20347/WIAS.PREPRINT.2880

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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