Periodic unfolding and Robin problems in perforated domains

Doina Cioranescu; Patrizia Donato; Rachad Zaki

doi:10.1016/j.crma.2006.01.028

Partial Differential Equations

Periodic unfolding and Robin problems in perforated domains

Presented by: Philippe G. Ciarlet

Doina Cioranescu ¹; Patrizia Donato ^1,²; Rachad Zaki ¹

¹ Université Pierre et Marie Curie (Paris VI), Laboratoire Jacques-Louis Lions, Case 187, 4, Place Jussieu, 75252 Paris Cedex 05, France
² Université de Rouen, Département de Mathématiques, avenue de l'Université, BP 12, 76801 Saint Etienne de Rouvray, France

Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 469-474.

Abstract
Résumé

The periodic unfolding method was introduced in 2002 by D. Cioranescu et al. for the study of classical periodic homogenization. In this Note, we extend this method to perforated domains introducing also a boundary unfolding operator. As an application, we study the homogenization of some elliptic problems with Robin condition on the boundary of the holes.

Dans cette Note nous adaptons la méthode d'éclatement périodique introduite par D. Cioranescu et al. en 2002 aux domaines perforés. Afin d'étudier des problèmes non homogènes, nous introduisons un opérateur d'éclatement frontière. Les résultats sont ensuite appliqués à l'homogénéisation de quelques problèmes elliptiques avec une condition du type Fourier sur le bord des trous.

Received: 2006-01-19
Accepted: 2006-01-26
Published online: 2006-03-06

DOI: 10.1016/j.crma.2006.01.028

Author's affiliations:

Doina Cioranescu ¹; Patrizia Donato ^{1, 2}; Rachad Zaki ¹

¹ Université Pierre et Marie Curie (Paris VI), Laboratoire Jacques-Louis Lions, Case 187, 4, Place Jussieu, 75252 Paris Cedex 05, France
² Université de Rouen, Département de Mathématiques, avenue de l'Université, BP 12, 76801 Saint Etienne de Rouvray, France

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     author = {Doina Cioranescu and Patrizia Donato and Rachad Zaki},
     title = {Periodic unfolding and {Robin} problems in perforated domains},
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     doi = {10.1016/j.crma.2006.01.028},
     language = {en},
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Doina Cioranescu; Patrizia Donato; Rachad Zaki. Periodic unfolding and Robin problems in perforated domains. Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 469-474. doi : 10.1016/j.crma.2006.01.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.01.028/

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