Date
1999
Indexation documentaire
Analyse
Subject
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 equations
Nom de la revue
Journal de mathématiques pures et appliquées
Volume
78
Numéro
2
Date de publication
1999
Pages article
121-157
Nom de l'éditeur
Elsevier
Type
Article accepté pour publication ou publié
Résumé en anglais
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.
