Homogenization of a nonstationary convection-diffusion equation in a thin rod and in a layer

Grégoire Allaire 1, 2 I. Pankratova 3, 4 Andrey Piatnitski 3, 5
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : The paper deals with the homogenization of a non-stationary convection-diffusion equation defined in a thin rod or in a layer with Dirichlet boundary condition. Under the assumption that the convection term is large, we describe the evolution of the solution’s profile and determine the rate of its decay. The main feature of our analysis is that we make no assumption on the support of the initial data which may touch the domain’s boundary. This requires the construction of boundary layer correctors in the homogenization process which, surprisingly, play a crucial role in the definition of the leading order term at the limit. Therefore we have to restrict our attention to simple geometries like a rod or a layer for which the definition of boundary layers is easy and explicit.
Type de document :
Article dans une revue
SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, Springer, 2012, 58 (1), pp.53-95. 〈10.1007/BF03322605〉
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Contributeur : Houssem Haddar <>
Soumis le : dimanche 3 février 2013 - 12:24:15
Dernière modification le : jeudi 10 mai 2018 - 02:05:57

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Grégoire Allaire, I. Pankratova, Andrey Piatnitski. Homogenization of a nonstationary convection-diffusion equation in a thin rod and in a layer. SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, Springer, 2012, 58 (1), pp.53-95. 〈10.1007/BF03322605〉. 〈hal-00784040〉

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