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drift-diffusion equation.

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation
Thierry Goudon, Antoine Mellet
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 9 / January 2003

Published online by Cambridge University Press:

15 September 2003, pp. 371-398

Print publication:

January 2003
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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.