| Issue |
ESAIM: M2AN
Volume 49, Number 1, January-February 2015
|
|
|---|---|---|
| Page(s) | 1 - 17 | |
| DOI | https://doi.org/10.1051/m2an/2014020 | |
| Published online | 12 January 2015 | |
Diffusion limit of Fokker−Planck equation with heavy tail equilibria∗
1 Institut de Mathématiques de
Toulouse, Université de Toulouse, 31062
Toulouse cedex 9,
France.
elissar.nasreddine@math.univ-toulouse.fr
2 Laboratoire Dieudonné, Université de
Nice Sophia Antipolis, Parc Valrose, 06108
Nice cedex 2,
France.
Marjolaine.Puel@unice.fr
Received:
17
May
2013
Revised:
17
February
2014
This paper is devoted to the diffusion limit of the Fokker−Planck equation of plasma physics, in which the equilibrium function decays towards zero at infinity like a negative power function. We prove that for an appropriate time scale, in a suitable weighted Sobolev space, the small mean free path limit gives rise to a diffusion equation.
Mathematics Subject Classification: 60J60 / 60J70 / 35Q84
Key words: Fokker Plank / diffusion limit / heavy tail / Cauchy distribution
© EDP Sciences, SMAI 2015
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