Construction of an eigen-solution for the Fokker-Planck operator with heavy tail equilibrium: an `a la Koch method in dimension 1

2023/03/13 by Dechicha, Dahmane, Puel, Marjolaine
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.07159

Abstract

This paper is devoted to the construction of an eigen-solution for the Fokker-Planck operator with heavy tail equilibrium. We propose an alternative method in dimension 1, which will be generalizable in higher dimension. The later method is inspired by the work of H. Koch on non-linear KdV equation \citeKoch. As a consequence of this construction, we recover the result of G. Lebeau and M. Puel \citeLebPu on the fractional diffusion limit for the Fokker-Planck equation.

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