In this talk, we review some aspects of the derivation of fractional diffusion equations from kinetic equations and in particular some applications to the description of anomalous energy transport in FPU chains. This is based on joint works with N. Ben Abdallah, L. Cesbron, S. Merino, S. Mischler, C. Mouhot and M. Puel
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.
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.
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