The role of a strong confining potential in a nonlinear Fokker-Planck equation
type: Item
instance of: scholarly article
title: The role of a strong confining potential in a nonlinear Fokker-Planck equation
zbMATH Open document ID: 1442.35023
author: Luca Alasio
author: Maria Bruna
author: J. A. Carrillo
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2020-04-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1807.11055
review text: The paper studies the connection between a class of nonlinear and nonlocal Fokker-Planck equation defined on a bounded domain with no-flux boundary condition with the the Cauchy problem of the same euqation but with a strong confinement potential. The authors show that the the solution of the problem can be obtained as the weak limit of the solution of the Cauchy problem as the confinement parameter tends to infinity. The proof relies on some uniform \(L^2\)-energy estimates and free energy estimates for nondegenerate and degenerate equations.
reviewed by: Yulong Lu
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35K61
Mathematics Subject Classification ID: 35Q84
zbMATH DE Number: 7187830
zbMATH Keywords: Fokker-Planck equations
zbMATH Keywords: nonlocal models
zbMATH Keywords: strong confinement
zbMATH Keywords: degenerate diffusion
MaRDI profile type: Publication
OpenAlex ID: W2963255288
arXiv ID: 1807.11055
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DOI: 10.1016/J.NA.2019.03.003
Wikidata QID: Q128129837
description: scientific article