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Elsevier, Journal de Mathématiques Pures et Appliquées, 2(78), p. 121-157, 1999

DOI: 10.1016/s0021-7824(01)80006-4

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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)

Journal article published in 1999 by J. Dolbeault ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

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. (C) Elsevier, Paris.