Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (Large time behavior and steady states)
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Date
1999Dewey
AnalyseSujet
Kinetic equations; Fokker-Planck equation; Vlasov equation; Poisson equation; Poisson-Boltzmann-Emden equation; Confinement; Stationary solutions; Long time asymptotics; Steady states; Renormalized solutions; A priori estimates; Entropy; Free energy; Configurational free energy; Jensen's inequality; Marcinkiewicz spaces; Semilinear elliptic equationsJournal issue
Journal de mathématiques pures et appliquéesVolume
78Number
2Publication date
1999Article pages
121-157Publisher
ElsevierCollections
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Dolbeault, Jean
Type
Abstract (EN)
This paper is devoted to the characterization of external electrostatic potentials for which the Vlasov-Poisson-Fokker-Planck system satisfies one of the following properties: (i) the system admits stationary solutions, (ii) any solution to the evolution problem converges to a stationary solution, or, equivalently, no mass vanishes for large times, (iii) the free energy is bounded from below, We give conditions under which these different notions of confinement are equivalent.Related items
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