Homogenization of periodic non self-adjoint problems with large drift and potential
ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 4, pp. 735-749.

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 ε -2 and the drift or first-order term is scaled as ε -1 . 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.

DOI: 10.1051/cocv:2007030
Classification: 35B27, 35K57, 35P15, 74Q10
Keywords: homogenization, non self-adjoint operators, convection-diffusion, periodic medium
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     title = {Homogenization of periodic non self-adjoint problems with large drift and potential},
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     pages = {735--749},
     publisher = {EDP-Sciences},
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Allaire, Grégoire; Orive, Rafael. Homogenization of periodic non self-adjoint problems with large drift and potential. ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 4, pp. 735-749. doi : 10.1051/cocv:2007030. http://archive.numdam.org/articles/10.1051/cocv:2007030/

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