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March  2008, 3(1): 97-124. doi: 10.3934/nhm.2008.3.97

Homogenization and correctors for the wave equation in non periodic perforated domains

Patrizia Donato 1, and  Florian Gaveau 2,

1. 

Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085, Avenue de l’Université, BP 12, 76801 Saint Etienne de Rouvray, France
2. 

Laboratoire Jacques-Louis Lions, UMR CNRS 7598, Université Paris 6 BP 187, 4 Place Jussieu 75252 Paris Cedex 05, France

Received  May 2007 Revised  October 2007 Published  January 2008

We consider here the wave equation in a (not necessarily periodic) perforated domain, with a Neumann condition on the boundary of the holes. Assuming $H^0$-convergence ([3]) on the elliptic part of the operator, we prove two main theorems: a convergence result and a corrector one. To prove the corrector result, we make use of a suitable family of elliptic local correctors given in [4] whose columns are piecewise locally square integrable gradients. As in the case without holes ([2]), some additional assumptions on the data are needed.
Keywords: wave equation., $H^0$-convergence, Homogenization, correctors.
Mathematics Subject Classification: Primary: 35B27; Secondary: 35L0.
Citation: Patrizia Donato, Florian Gaveau. Homogenization and correctors for the wave equation in non periodic perforated domains. Networks & Heterogeneous Media, 2008, 3 (1) : 97-124. doi: 10.3934/nhm.2008.3.97
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