Issue |
ESAIM: COCV
Volume 13, Number 4, October-December 2007
|
|
---|---|---|
Page(s) | 735 - 749 | |
DOI | https://doi.org/10.1051/cocv:2007030 | |
Published online | 20 July 2007 |
Homogenization of periodic non self-adjoint problems with large drift and potential
1
Centre de Mathématiques
Appliquées, École Polytechnique, 91128 Palaiseau Cedex, Paris, France; gregoire.allaire@polytechnique.fr
2
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049
Madrid, Spain; rafael.orive@uam.es
Received:
11
July
2005
Revised:
29
June
2006
We consider the homogenization of both the parabolic and eigenvalue problems for a singularly perturbed
convection-diffusion equation in a periodic medium. All coefficients of the equation may vary both on the
macroscopic scale and on the periodic microscopic scale. Denoting by ε the period, the potential or zero-order
term is scaled as and the drift or first-order term is scaled as
. Under a structural
hypothesis on the first cell eigenvalue, which is assumed to admit a unique minimum in the domain with
non-degenerate quadratic behavior, we prove an exponential localization at this minimum point. The homogenized
problem features a diffusion equation with quadratic potential in the whole space.
Mathematics Subject Classification: 35B27 / 35K57 / 35P15 / 74Q10
Key words: Homogenization / non self-adjoint operators / convection-diffusion / periodic medium
© EDP Sciences, SMAI, 2007
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