Homogenization and singular perturbation in porous media

Eduard Marušić-Paloka; Igor Pažanin

doi:10.3934/cpaa.2020279

Article Contents

2021, Volume 20, Issue 2: 533-545. Doi: 10.3934/cpaa.2020279

This issue Previous Article Topological Equivalence of nonautonomous difference equations with a family of dichotomies on the half line Next Article A unique continuation property for a class of parabolic differential inequalities in a bounded domain

Homogenization and singular perturbation in porous media

Eduard Marušić-Paloka^, and
Igor Pažanin

Departmant of mathematics, University of Zagreb, Bijenička 30, 10000, Zagreb, Croatia

^* Corresponding author
^* Corresponding author

Received: April 2020

Revised: September 2020

Early access: December 2020

Published: February 2021

The authors of this work have been supported by the Croatian Science Foundation (grant: 2735 Asymptotic analysis of the boundary value problems in continuum mechanics - AsAn).

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Abstract

We study a Dirichlet problem in periodic porous medium depending on two small parameters, the hydraulic permeability of the porous inclusions $ \delta $ and the period $ \varepsilon $. We study the situation as $ \delta\to 0 \;, \; \varepsilon\to 0 $ and $ \varepsilon \to 0 \;, \; \delta\to 0 $ and prove that the two limits do not commute.

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Mathematics Subject Classification: Primary: 35B27, 76M50; Secondary: 35Q30.

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