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

Published online by Cambridge University Press:  17 May 2011

T. L. VAN NOORDEN  and
A. MUNTEAN
T. L. VAN NOORDEN
Affiliation:
Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands email: [email protected]
A. MUNTEAN
Affiliation:
Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands email: [email protected] Institute of Complex Molecular Systems (ICMS), Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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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∞-bounds, uniqueness, energy inequality) are obtained in the x-dependent Bochner spaces.

Keywords

Heterogeneous porous materialsLocally periodic homogenisationMicro–macro transportTwo-scale modelReaction–diffusion systemWeak solvability
Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 5 , October 2011 , pp. 493 - 516
Copyright
Copyright © Cambridge University Press 2011

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