Volume 13, Number 4, October-December 2007
|Page(s)||735 - 749|
|Published online||20 July 2007|
Homogenization of periodic non self-adjoint problems with large drift and potential
Centre de Mathématiques
Appliquées, École Polytechnique, 91128 Palaiseau Cedex, Paris, France; firstname.lastname@example.org
2 Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain; email@example.com
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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