[Homogénéisation d'une classe d'équations elliptiques non linéaires de croissance non standard]
On étudie l'homogénéisation du problème variationnel de Dirichlet d'une classe d'équations elliptiques non linéaires de croissance non standard. Ce genre d'équations apparaît dans la modélisation de certains problèmes de l'ingénierie, comme par exemple les fluides électrorhéologiques, les écoulements non Newtoniens thermoconvectifs, et les écoulements non linéaires de Darcy de fluides compressibles en milieux poreux hétérogènes. On obtient le problème homogénéisé par la technique de l'homogénéisation variationnelle dans le cadre des espaces de Sobolev avec des exposants variables. Enfin, on présente un exemple périodique pour illustrer le résultat obtenu.
We study the homogenization of the Dirichlet variational problem of a class of nonlinear elliptic equations with nonstandard growth. Such equations arise in many engineering disciplines, such as electrorheological fluids, non-Newtonian fluids with thermo-convective effects, and nonlinear Darcy flow of compressible fluids in heterogeneous porous media. We derive the homogenized model by means of the variational homogenization technique in the framework of Sobolev spaces with variable exponents. This result is then illustrated with a periodic example.
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Mot clés : Mécanique des fluides, Homogénéisation, Problème variationnel non linéaire, Croissance non standard
@article{CRMECA_2007__335_3_138_0,
author = {Brahim Amaziane and Stanislav Antontsev and Leonid Pankratov},
title = {Homogenization of a class of nonlinear elliptic equations with nonstandard growth},
journal = {Comptes Rendus. M\'ecanique},
pages = {138--143},
publisher = {Elsevier},
volume = {335},
number = {3},
year = {2007},
doi = {10.1016/j.crme.2007.02.007},
language = {en},
}
TY - JOUR AU - Brahim Amaziane AU - Stanislav Antontsev AU - Leonid Pankratov TI - Homogenization of a class of nonlinear elliptic equations with nonstandard growth JO - Comptes Rendus. Mécanique PY - 2007 SP - 138 EP - 143 VL - 335 IS - 3 PB - Elsevier DO - 10.1016/j.crme.2007.02.007 LA - en ID - CRMECA_2007__335_3_138_0 ER -
%0 Journal Article %A Brahim Amaziane %A Stanislav Antontsev %A Leonid Pankratov %T Homogenization of a class of nonlinear elliptic equations with nonstandard growth %J Comptes Rendus. Mécanique %D 2007 %P 138-143 %V 335 %N 3 %I Elsevier %R 10.1016/j.crme.2007.02.007 %G en %F CRMECA_2007__335_3_138_0
Brahim Amaziane; Stanislav Antontsev; Leonid Pankratov. Homogenization of a class of nonlinear elliptic equations with nonstandard growth. Comptes Rendus. Mécanique, Volume 335 (2007) no. 3, pp. 138-143. doi : 10.1016/j.crme.2007.02.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.02.007/
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