# American Institute of Mathematical Sciences

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

 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.
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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