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.
Mots-clés : Boltzmann equation, diffusion approximation, homogenization, drift-diffusion equation
@article{COCV_2003__9__371_0,
author = {Goudon, Thierry and Mellet, Antoine},
title = {Homogenization and diffusion asymptotics of the linear {Boltzmann} equation},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {371--398},
publisher = {EDP-Sciences},
volume = {9},
year = {2003},
doi = {10.1051/cocv:2003018},
mrnumber = {1988668},
zbl = {1070.35032},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2003018/}
}
TY - JOUR AU - Goudon, Thierry AU - Mellet, Antoine TI - Homogenization and diffusion asymptotics of the linear Boltzmann equation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2003 SP - 371 EP - 398 VL - 9 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2003018/ DO - 10.1051/cocv:2003018 LA - en ID - COCV_2003__9__371_0 ER -
%0 Journal Article %A Goudon, Thierry %A Mellet, Antoine %T Homogenization and diffusion asymptotics of the linear Boltzmann equation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 371-398 %V 9 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2003018/ %R 10.1051/cocv:2003018 %G en %F COCV_2003__9__371_0
Goudon, Thierry; Mellet, Antoine. Homogenization and diffusion asymptotics of the linear Boltzmann equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 371-398. doi : 10.1051/cocv:2003018. http://www.numdam.org/articles/10.1051/cocv:2003018/
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