Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (large time behavior and steady states)
type: Item
instance of: scholarly article
title: Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (large time behavior and steady states)
zbMATH Open document ID: 1115.82316
DOI: 10.1016/S0021-7824(01)80006-4
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1999-10-05T00:00:00Z
Mathematics Subject Classification ID: 82B40
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1344444
zbMATH Keywords: Kinetic equations
zbMATH Keywords: Fokker-Planck equation
zbMATH Keywords: Vlasov equation
zbMATH Keywords: Poisson equation
zbMATH Keywords: Poisson-Boltzmann-Emden equation
zbMATH Keywords: Confinement
zbMATH Keywords: Stationary solutions
zbMATH Keywords: Long time asymptotics
zbMATH Keywords: Steady states
zbMATH Keywords: Renormalized solutions
zbMATH Keywords: A priori estimates
zbMATH Keywords: Entropy
zbMATH Keywords: Free energy
zbMATH Keywords: Configurational free energy
zbMATH Keywords: Jensen's inequality
zbMATH Keywords: Marcinkiewicz spaces
zbMATH Keywords: Semilinear elliptic equations
author: Jean Dolbeault
MaRDI profile type: Publication
cites work: Global weak solution of the vlasov–poisson system for small electrons mass
cites work: Existence and uniqueness of a global smooth solution for the Vlasov- Poisson-Fokker-Planck system in three dimensions
cites work: On long time asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with Coulombic and Newtonian potentials
cites work: Q5539510
cites work: Global solutions of Boltzmann's equation and the entropy inequality
cites work: Q4731530
cites work: STATIONARY STATES IN PLASMA PHYSICS: MAXWELLIAN SOLUTIONS OF THE VLASOV-POISSON SYSTEM
cites work: Stationary solutions of the vlasov-fokker-planck equation
cites work: Steady states in plasma physics—the Vlasov-Fokker-Planck equation
cites work: Sur les états d'équilibre pour les densités électroniques dans les plasmas
cites work: Steady states of the Vlasov-Poisson-Fokker-Planck system
cites work: Sur l'inégalité logarithmique de Sobolev
cites work: Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation
full work available at URL: s0021-7824(01)80006-4
OpenAlex ID: W1963509441
description: scientific article; zbMATH DE number 1344444