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Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation

Published online by Cambridge University Press:  15 September 2003

Thierry Goudon  and
Antoine Mellet
Thierry Goudon
Affiliation:
CNRS, Université des Sciences et Technologies Lille 1, UFR Mathématiques Pures et Appliquées, Cité Scientifique, 59655 Villeneuve-d'Ascq Cedex, France; thierry.goudon@univ-lille1.fr. INRIA-Sophia, Project Caiman.
Antoine Mellet
Affiliation:
Mathématiques pour l'Industrie et la Physique, UMR 5640, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France; mellet@mip.ups-tlse.fr.
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Abstract

We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.

Keywords

Boltzmann equationdiffusion approximationhomogenizationdrift-diffusion equation.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 9 , January 2003 , pp. 371 - 398
Copyright
© EDP Sciences, SMAI, 2003

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