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arXiv · 2303.07159

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

Dahmane Dechicha·Marjolaine Puel
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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.

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Dahmane Dechicha, Marjolaine Puel. 2023-03-13. Construction of an eigen-solution for the Fokker-Planck operator with heavy tail equilibrium: an `a la Koch method in dimension 1. https://arxiv.org/abs/2303.07159

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