| Issue |
ESAIM: COCV
Volume 9, February 2003
|
|
|---|---|---|
| Page(s) | 371 - 398 | |
| DOI | https://doi.org/10.1051/cocv:2003018 | |
| Published online | 15 September 2003 | |
Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation
1
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.
2
INRIA-Sophia, Project Caiman.
3
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.
Received:
30
September
2002
Revised:
4
March
2003
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.
Mathematics Subject Classification: 35Q35 / 82C70 / 76P05 / 74Q99 / 35B27
Key words: Boltzmann equation / diffusion approximation / homogenization / drift-diffusion equation.
© EDP Sciences, SMAI, 2003
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