Homogenization and singular perturbation in porous media

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.