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Distributed microstructure models of porous media. (English) Zbl 0805.76082

Douglas, J. jun. (ed.) et al., Flow in porous media. Proceedings of the Oberwolfach conference, Oberwolfach, Germany, June 21-27, 1992. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 114, 159-163 (1993).
Summary: Laminar flow through fissured or otherwise highly inhomogeneous media leads to very singular initial-boundary value problems for equations with rapidly oscillating coefficients. The limiting case (by homogeneization) is a continuous distribution of model cells which represent a valid approximation of the finite (singular) case, and we survey some recent results on the theory of such systems. This is developed as an application of continuous direct sums of Banach spaces which arise rather naturally as the energy or state spaces for the corresponding (stationary) variational or (temporal) dynamic problems. We discuss the basic models for a totally fissured medium, the extension to include secondary flux in partially fissured media, and the classical model systems which are realized as limiting cases of the microstructure models.
For the entire collection see [Zbl 0795.00022].

MSC:

76S05 Flows in porous media; filtration; seepage
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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