Diffusion of a single-phase fluid through a general deterministic partially-fissured medium
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 s...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/164/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |