Archive for Rational Mechanics and Analysis

, Volume 199, Issue 2, pp 493–525

Fractional Diffusion Limit for Collisional Kinetic Equations

  • Antoine Mellet
  • Stéphane Mischler
  • Clément Mouhot
Article

DOI: 10.1007/s00205-010-0354-2

Cite this article as:
Mellet, A., Mischler, S. & Mouhot, C. Arch Rational Mech Anal (2011) 199: 493. doi:10.1007/s00205-010-0354-2

Abstract

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.

Download to read the full article text

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Antoine Mellet
    • 1
  • Stéphane Mischler
    • 2
    • 3
  • Clément Mouhot
    • 4
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.CEREMADEUniversité Paris-DauphineParisFrance
  3. 3.Cambridge UniversityCambridgeUK
  4. 4.DMA, ÉNSParisFrance

Personalised recommendations