# Homogenization of periodic non self-adjoint problems with large drift and potential

Grégoire Allaire; Rafael Orive

ESAIM: Control, Optimisation and Calculus of Variations (2007)

- Volume: 13, Issue: 4, page 735-749
- ISSN: 1292-8119

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topAllaire, Grégoire, and Orive, Rafael. "Homogenization of periodic non self-adjoint problems with large drift and potential." ESAIM: Control, Optimisation and Calculus of Variations 13.4 (2007): 735-749. <http://eudml.org/doc/250000>.

@article{Allaire2007,

abstract = {
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 $\varepsilon^\{-2\}$ and the drift or first-order term is scaled as $\varepsilon^\{-1\}$. 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.
},

author = {Allaire, Grégoire, Orive, Rafael},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Homogenization; non self-adjoint operators; convection-diffusion; periodic medium},

language = {eng},

month = {7},

number = {4},

pages = {735-749},

publisher = {EDP Sciences},

title = {Homogenization of periodic non self-adjoint problems with large drift and potential},

url = {http://eudml.org/doc/250000},

volume = {13},

year = {2007},

}

TY - JOUR

AU - Allaire, Grégoire

AU - Orive, Rafael

TI - Homogenization of periodic non self-adjoint problems with large drift and potential

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2007/7//

PB - EDP Sciences

VL - 13

IS - 4

SP - 735

EP - 749

AB -
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 $\varepsilon^{-2}$ and the drift or first-order term is scaled as $\varepsilon^{-1}$. 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.

LA - eng

KW - Homogenization; non self-adjoint operators; convection-diffusion; periodic medium

UR - http://eudml.org/doc/250000

ER -

## References

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