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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
1999
Dewey
Analyse
Sujet
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
Journal issue
Journal de mathématiques pures et appliquées
Volume
78
Number
2
Publication date
1999
Article pages
121-157
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/S0021-7824(01)80006-4
URI
https://basepub.dauphine.fr/handle/123456789/6458
Collections
  • CEREMADE : Publications
Metadata
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Author
Dolbeault, Jean
Type
Article accepté pour publication ou publié
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.

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