Uniform semigroup spectral analysis of the discrete, fractional and classical Fokker-Planck equations
type: Item
instance of: scholarly article
title: Uniform semigroup spectral analysis of the discrete, fractional and classical Fokker-Planck equations
zbMATH Open document ID: 1420.47026
author: Stéphane Mischler
author: Isabelle Tristani
publication date: 2017-07-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/1507.04861
review text: In this interesting paper, the authors investigate the spectral analysis and long time asymptotic convergence of semigroups associated to discrete, fractional and classical Fokker-Planck equations. We recall that Fokker-Planck equations model time evolution of a density function of particles undergoing both diffusion and (harmonic) confinement mechanisms. They prove that the convergence is exponentially fast for a large class of initial data taken in a fixed weighted Lebesgue or weighted Sobolev space, with a rate of convergence which can be chosen uniformly with respect to the diffusion term. They investigate three regimes where these diffusion operators are close and for which such a uniform convergence can be established. The proofs are based on a deep and innovative splitting of the generator method.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35Q84
zbMATH DE Number: 6754331
zbMATH Keywords: Fokker-Planck equation
zbMATH Keywords: fractional Laplacian
zbMATH Keywords: spectral gap
zbMATH Keywords: exponential rate of convergence
zbMATH Keywords: long-time asymptotic
zbMATH Keywords: semigroup
zbMATH Keywords: dissipativity
MaRDI profile type: Publication
OpenAlex ID: W876269324
arXiv ID: 1507.04861
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DOI: 10.5802/JEP.46
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published in: Journal de l’École polytechnique — Mathématiques
description: scientific article