Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (Large time behavior and steady states)
Dolbeault, Jean (1999), Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (Large time behavior and steady states), Journal de mathématiques pures et appliquées, 78, 2, p. 121-157. http://dx.doi.org/10.1016/S0021-7824(01)80006-4
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Article accepté pour publication ou publiéDate
1999Journal name
Journal de mathématiques pures et appliquéesVolume
78Number
2Publisher
Elsevier
Pages
121-157
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Show full item recordAbstract (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.Subjects / Keywords
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 equationsRelated items
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