Nonlinear double porosity models with non-standard growth

Catherine Choquet; Leonid Pankratov

doi:10.1016/j.crme.2009.09.004

Nonlinear double porosity models with non-standard growth
[Modèles non linéaires de type double-porosité à croissance non standart]

Présenté par : Évariste Sanchez-Palencia

Catherine Choquet ¹ ; Leonid Pankratov ²

¹ Université P. Cézanne, LATP UMR 6632, and Délégation CNRS LAMA UMR 5127, université de Savoie; FST, case cour A, 13397 Marseille cedex 20, France
² Mathematical Division, Institute for Low Temperature Physics, 47, Lenin ave., 310164 Kharkov, Ukraine

Comptes Rendus. Mécanique, Volume 337 (2009) no. 9-10, pp. 659-666.

Résumé
Abstract

Nous étudions les solutions d'équations quasilinéaires elliptiques à coefficients fortement contrastés. La formulation variationnelle associée conduit à travailler dans des espaces de Lebesgue à exposant variable $L^{p_{ε} (\cdot)}$ dans des domaines à la microstructure complexe caractérisée par un petit paramètre ε. Nous obtenons rigoureusement le problème homogénéisé correspondant. Il est déterminé par les caractéristiques variationnelles locales de la microstructure.

We study the solutions to quasilinear elliptic equations with high contrast coefficients. The energy formulation leads to work with variable exponent Lebesgue spaces $L^{p_{ε} (\cdot)}$ in domains with a complex microstructure scaled by a small parameter ε. We derive rigorously the corresponding homogenized problem. It is completely described in terms of local energy characteristics of the original domain.

Reçu le : 2009-06-24
Accepté le : 2009-08-31
Publié le : 2009-09-01

DOI : 10.1016/j.crme.2009.09.004

Keywords: Fluid mechanics, Homogenization, Double porosity, Non-standard growth
Mots-clés : Mécanique des fluides, Homogénéisation, Double porosité, Croissance non standard

Affiliations des auteurs :

Catherine Choquet ¹ ; Leonid Pankratov ²

¹ Université P. Cézanne, LATP UMR 6632, and Délégation CNRS LAMA UMR 5127, université de Savoie; FST, case cour A, 13397 Marseille cedex 20, France
² Mathematical Division, Institute for Low Temperature Physics, 47, Lenin ave., 310164 Kharkov, Ukraine

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Catherine Choquet; Leonid Pankratov. Nonlinear double porosity models with non-standard growth. Comptes Rendus. Mécanique, Volume 337 (2009) no. 9-10, pp. 659-666. doi : 10.1016/j.crme.2009.09.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.09.004/

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Brahim Amaziane; Leonid Pankratov Homogenization in Sobolev Spaces with Nonstandard Growth: Brief Review of Methods and Applications, International Journal of Differential Equations, Volume 2013 (2013), p. 1 | DOI:10.1155/2013/693529

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