Relative entropies for the Vlasov-Poisson system in bounded domains;Entropies relatives pour le système de Vlasov-Poisson dans des domaines bornés

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 330, Issue 10, 2000, Pages 867-872

  Abdallah, Naoufel Ben ^a   Dolbeault, Jean ^b  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17944383995     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0764-4442(00)00268-8     Document Type: Article

References (12)

1. [1] Arnold A., Markowich P., Toscani G., Unterreiter A., On logarithmic Sobolev inequalities, Csiszár-Kullback inequalities, and the rate of convergence to equilibrium for Fokker-Planck type equations, Preprint T.M.R. "Asymptotic Methods in Kinetic Theory" n° 1, 1998.
2. [2] Ben Abdallah N., Dolbeault J., (in preparation).
3. [3] Benachour S., Analyticité des solutions des équations de Vlassov-Poisson, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4nd series) 16 (1) (1989) 83-104.
4. [4] Bonilla L.L., Carrillo J.A., Soler J., Asymptotic behaviour of the initial boundary value problem for the three-dimensional Vlasov-Poisson-Fokker-Planck system, SIAM J. Appl. Math. 57 (1997) 1343-1372.
5. [5] Caglioti E., Maffei C., Time asymptotics for solutions of Vlasov-Poisson equation in a circle, J. Statis. Phys. 92 (1-2) (1998) 301-323.
6. [6] Carrillo J.A., Global weak solutions for the initial-boundary value problems to the Vlasov-Poisson-Fokker-Planck system, Math. Meth. Appl. Sci. 21 (1998) 907-938.
7. [7] Degond P., Spectral theory of the linearized Vlasov-Poisson equation, Trans. Amer. Math. Soc. 294 (2) (1986) 435-453.
8. [8] Desvillettes L., Villani C., On the trend to golbal equilibrium in spatially inhomogeneous entropy-dissipating systems, Part I: the linear Fokker-Planck equation, Preprint TMR "Asymptotic Methods in Kinetic Theory" n° 79, 1999.
9. [9] Dolbeault J., Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (large time behavior and steady states), J. Math. Pures et Appl. 78 (1999) 121-157.
10. [10] Glassey R., Schaeffer J., On time decay rates in Landau damping, Commun. Partial Differ. Eq. 20 (3-4) (1995) 647-676.
11. [11] Mischler S., On the trace problem for solutions of the Vlasov equation, Commun. Partial Differ. Eq. (2000) (to appear).
12. [12] Poupaud F., Boundary value problems for the stationary Vlasov-Maxwell system, Forum Math. 4 (1992) 499-527.