Homogenization and diffusion asymptotics of the linear Boltzmann equation

Goudon, Thierry; Mellet, Antoine

ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 371-398.

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.

Classification : 35Q35, 82C70, 76P05, 74Q99, 35B27
Mots clés : Boltzmann equation, diffusion approximation, homogenization, drift-diffusion equation

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