Diffusion limit of Fokker−Planck equation with heavy tail equilibria
Nasreddine, Elissar1 ; Puel, Marjolaine2
1 Institut de Mathématiques de Toulouse, Université de Toulouse, 31062 Toulouse cedex 9, France.
2 Laboratoire Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice cedex 2, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 1, pp. 1-17.

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.

DOI : 10.1051/m2an/2014020
Classification : 60J60, 60J70, 35Q84
Mots-clés : Fokker Plank, diffusion limit, heavy tail, Cauchy distribution
Nasreddine, Elissar 1 ; Puel, Marjolaine 2

1 Institut de Mathématiques de Toulouse, Université de Toulouse, 31062 Toulouse cedex 9, France.
2 Laboratoire Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice cedex 2, France. 
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Nasreddine, Elissar; Puel, Marjolaine. Diffusion limit of Fokker−Planck equation with heavy tail equilibria. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 1, pp. 1-17. doi : 10.1051/m2an/2014020. http://www.numdam.org/articles/10.1051/m2an/2014020/

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