Electron. J. Diff. Equ., Vol. 2014 (2014), No. 164, pp. 1-26.

Diffusion of a single-phase fluid through a general deterministic partially-fissured medium

Gabriel Nguetseng, Ralph E. Showalter, Jean Louis Woukeng

The sigma convergence method was introduced by G. Nguetseng for studying deterministic homogenization problems beyond the periodic setting and extended by him to the case of deterministic homogenization in general deterministic perforated domains. Here we show that this concept can also model such problems in more general domains. We illustrate this by considering the quasi-linear version of the distributed-microstructure model for single phase fluid flow in a partially fissured medium. We use the well-known concept of algebras with mean value. An important result of de Rham type is first proven in this setting and then used to get a general compactness result associated to algebras with mean value in the framework of sigma convergence. Finally we use these results to obtain homogenized limits of our micro-model in various deterministic settings, including periodic and almost periodic cases.

Submitted March 26, 2014. Published July 30, 2014.
Math Subject Classifications: 35A15, 35B40, 46J10, 76S05.
Key Words: General deterministic fissured medium; homogenization; algebras with mean value; sigma convergence.

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Gabriel Nguetseng
Department of Mathematics, University of Yaounde 1
P.O. Box 812, Yaounde, Cameroon
email: nguetseng@uy1.uninet.cm
Ralph E. Showalter
Department of Mathematics, Oregon State University
Corvallis, OR 97331-4605, USA
email: show@math.oregonstate.edu
Jean Louis Woukeng
Department of Mathematics and Computer Science
University of Dschang
P.O. Box 67, Dschang, Cameroon
email: jwoukeng@yahoo.fr

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