This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation. © 2010 Springer-Verlag.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: ANTOINE MELLET gratefully thanks the CEREMADE at the Universite Paris Dauphine, where most of this research was performed, for its hospitality. ANTOINE MELLET was also partially supported by NSERC Grant 341253-07. CLEMENT MOUHOT would like to thank Cambridge University who provided repeated hospitality in 2009 and 2010 thanks to the Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST). The authors thank JEAN DOLBEAULT AND STEFANO OLLA for fruitful discussions during the preparation of this work.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.