Homogenization and diffusion asymptotics of the linear Boltzmann equation

Thierry Goudon; Antoine Mellet

ESAIM: Control, Optimisation and Calculus of Variations (2003)

  • Volume: 9, page 371-398
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Goudon, Thierry, and Mellet, Antoine. "Homogenization and diffusion asymptotics of the linear Boltzmann equation." ESAIM: Control, Optimisation and Calculus of Variations 9 (2003): 371-398. <http://eudml.org/doc/245318>.

@article{Goudon2003,
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.},
author = {Goudon, Thierry, Mellet, Antoine},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Boltzmann equation; diffusion approximation; homogenization; drift-diffusion equation; semiconductors},
language = {eng},
pages = {371-398},
publisher = {EDP-Sciences},
title = {Homogenization and diffusion asymptotics of the linear Boltzmann equation},
url = {http://eudml.org/doc/245318},
volume = {9},
year = {2003},
}

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
PB - EDP-Sciences
VL - 9
SP - 371
EP - 398
AB - 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.
LA - eng
KW - Boltzmann equation; diffusion approximation; homogenization; drift-diffusion equation; semiconductors
UR - http://eudml.org/doc/245318
ER -

References

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