Gabriel Nguetseng, Ralph E. Showalter, Jean Louis Woukeng
Abstract:
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.
Show me the PDF file (389 KB), TEX file, and other files for this article.
 |
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 |
Return to the EJDE web page