Construction of an eigen-solution for the Fokker-Planck operator with heavy tail equilibrium: an `a la Koch method in dimension 1
Analysis of PDEs
2023-03-14 v1
Abstract
This paper is devoted to the construction of an \emph{eigen-solution} for the Fokker-Planck operator with heavy tail equilibrium. We propose an \textit{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 \cite{Koch}. As a consequence of this construction, we recover the result of G. Lebeau and M. Puel \cite{LebPu} on the fractional diffusion limit for the Fokker-Planck equation.
Keywords
Cite
@article{arxiv.2303.07159,
title = {Construction of an eigen-solution for the Fokker-Planck operator with heavy tail equilibrium: an `a la Koch method in dimension 1},
author = {Dahmane Dechicha and Marjolaine Puel},
journal= {arXiv preprint arXiv:2303.07159},
year = {2023}
}