Homogenization and concentration for a diffusion equation with large convection in a bounded domain

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 : We consider the homogenization of a non-stationary convection–diffusion equation posed in a bounded domain with periodically oscillating coefficients and homogeneous Dirichlet boundary conditions. Assuming that the convection term is large, we give the asymptotic profile of the solution and determine its rate of decay. In particular, it allows us to characterize the “hot spot”, i.e., the precise asymptotic location of the solution maximum which lies close to the domain boundary and is also the point of concentration. Due to the competition between convection and diffusion, the position of the “hot spot” is not always intuitive as exemplified in some numerical tests.
Type de document :
Article dans une revue
Journal of Functional Analysis, Elsevier, 2012, 262 (1), pp.300-330. 〈10.1016/j.jfa.2011.09.014〉
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Soumis le : dimanche 3 février 2013 - 12:28:57
Dernière modification le : jeudi 10 mai 2018 - 02:04:12

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Grégoire Allaire, I. Pankratova, Andrey Piatnitski. Homogenization and concentration for a diffusion equation with large convection in a bounded domain. Journal of Functional Analysis, Elsevier, 2012, 262 (1), pp.300-330. 〈10.1016/j.jfa.2011.09.014〉. 〈hal-00784043〉

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