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.
Mots clés : Fokker Plank, diffusion limit, heavy tail, Cauchy distribution
@article{M2AN_2015__49_1_1_0, author = {Nasreddine, Elissar and Puel, Marjolaine}, title = {Diffusion limit of {Fokker\ensuremath{-}Planck} equation with heavy tail equilibria}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1--17}, publisher = {EDP-Sciences}, volume = {49}, number = {1}, year = {2015}, doi = {10.1051/m2an/2014020}, mrnumber = {3342190}, zbl = {1319.35269}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2014020/} }
TY - JOUR AU - Nasreddine, Elissar AU - Puel, Marjolaine TI - Diffusion limit of Fokker−Planck equation with heavy tail equilibria JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 1 EP - 17 VL - 49 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014020/ DO - 10.1051/m2an/2014020 LA - en ID - M2AN_2015__49_1_1_0 ER -
%0 Journal Article %A Nasreddine, Elissar %A Puel, Marjolaine %T Diffusion limit of Fokker−Planck equation with heavy tail equilibria %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 1-17 %V 49 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014020/ %R 10.1051/m2an/2014020 %G en %F M2AN_2015__49_1_1_0
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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