Geodesic
Diffusion of a single-phase fluid through a general deterministic partially-fissured medium
Electronic journal of differential equations, Tome 2014 (2014)
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.
Classification : 35A15, 35B40, 46J10, 76S05
Keywords: general deterministic fissured medium, homogenization, algebras with mean value, sigma convergence 
@article{EJDE_2014__2014__a142,
     author = {Nguetseng,  Gabriel and Showalter,  Ralph E. and Woukeng,  Jean Louis},
     title = {Diffusion of a single-phase fluid through a general deterministic partially-fissured medium},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1297.35024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a142/}
}
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AU  - Woukeng,  Jean Louis
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JO  - Electronic journal of differential equations
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%A Woukeng,  Jean Louis
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%J Electronic journal of differential equations
%D 2014
%V 2014
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%G en
%F EJDE_2014__2014__a142
Nguetseng,  Gabriel; Showalter,  Ralph E.; Woukeng,  Jean Louis. Diffusion of a single-phase fluid through a general deterministic partially-fissured medium. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a142/