On a class of Fokker-Planck equations with subcritical confinement
type: Item
instance of: scholarly article
title: On a class of Fokker-Planck equations with subcritical confinement
zbMATH Open document ID: 1491.82016
DOI: 10.4171/RLM/944
author: M. Zanella
author: G. Toscani
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2022-02-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/2103.11146
review text: Summary: We study the relaxation to equilibrium for a class of linear one-dimensional Fokker-Planck equations characterized by a particular subcritical confinement potential. An interesting feature of this class of Fokker-Planck equations is that, for any given probability density \(e(x)\), the diffusion coefficient can be built to have \(e(x)\) as steady state. This representation of the equilibrium density can be fruitfully used to obtain one-dimensional Wirtinger-type inequalities and to recover, for a sufficiently regular density \(e(x)\), a polynomial rate of convergence to equilibrium. Numerical results then confirm the theoretical analysis, and allow to conjecture that convergence to equilibrium with positive rate still holds for steady states characterized by a very slow polynomial decay at infinity.
Mathematics Subject Classification ID: 82C31
Mathematics Subject Classification ID: 35Q84
Mathematics Subject Classification ID: 35Q82
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 82M20
Mathematics Subject Classification ID: 65D32
zbMATH DE Number: 7473889
zbMATH Keywords: Fokker-Planck equations
zbMATH Keywords: relative entropy
zbMATH Keywords: Wirtinger-type inequalities
zbMATH Keywords: relaxation to equilibrium
MaRDI profile type: Publication
arXiv ID: 2103.11146
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OpenAlex ID: W3138251849
description: scientific article