Volume 49, Number 1, January-February 2015
|Page(s)||1 - 17|
|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,
2 Laboratoire Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice cedex 2, France.
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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