Homogenisation of a locally-periodic medium with areas of low and high diffusivity

T.L. Noorden, van, A. Muntean

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33 Citations (Scopus)

Abstract

We aim at understanding transport in porous materials consisting of regions with both high and low diffusivities. We apply a formal homogenisation procedure to the case where the heterogeneities are not arranged in a strictly periodic manner. The result is a two-scale model formulated in x-dependent Bochner spaces. We prove the weak solvability of the limit two-scale model for a prototypical advection–diffusion system of minimal size. A special feature of our analysis is that most of the basic estimates (positivity, $L^\infty$-bounds, uniqueness, energy inequality) are obtained in $x$-dependent Bochner spaces.
Original languageEnglish
Pages (from-to)493-516
JournalEuropean Journal of Applied Mathematics
Volume22
Issue number5
DOIs
Publication statusPublished - 2011

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