172
Views
34
CrossRef citations to date
0
Altmetric
Original Articles

Equilibration Rate for the Linear Inhomogeneous Relaxation-Time Boltzmann Equation for Charged Particles

, &
Pages 969-989 | Received 01 Dec 2001, Published online: 14 Feb 2007

References

  • Arnold , A. , Markowich , P. , Toscani , G. and Unterreiter , A. 2001 . On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations . Comm. Partial Differential Equations , 26 ( 1–2 ) : 43 – 100 .
  • Bakry , D. and Emery , M. 1985 . “ Diffusions hypercontractives ” . In Séminaires de Probabilités, XIX, 1983–1984 , Lecture Notes in Math. Vol. 123 , 177 – 206 . Springer .
  • Ben Abdallah , N. and Dolbeault , J. 2000 . Entropies relatives pour le système de Vlasov-Poisson dans des domaines bornés (Relative entropies for the Vlasov-Poisson system in bounded domains) . C. R. Acad. Sci. Paris. Sér. I, Math. , 330 : 867 – 872 .
  • Ben Abdallah , N. and Dolbeault , J. Relative entropies for kinetic equations in bounded domains (irreversibility, stationary solutions, uniqueness) . To appear in Arch. Ratio. Mech. Anal.
  • Carrillo , J. A. , Jüngel , A. , Markowich , P. , Toscani , G. and Unterreiter , A. 2001 . Entropy dissipation methods for degenerate parabolic systems and generalized Sobolev inequalities . Monatsh. Math. , 133 : 1 – 82 .
  • Carrillo , J. A. , McCann , R. J. and Villani , C. Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates . To appear in Revista Matemática Iberoamericana
  • Carrillo , J. A. and Toscani , G. 2000 . Asymptotic L 1-decay of solutions of the porous medium equation to self-similarity . Indiana Univ. Math. J. , 49 : 113 – 141 .
  • Desvillettes , L. 1995 . About the regularizing properties of the non-cut-off Kac equation . Comm. Math. Phys. , 168 ( 2 ) : 417 – 440 .
  • Desvillettes , L. and Dolbeault , J. 1991 . On long time asymptotics of the Vlasov-Poisson-Boltzmann equation . Comm. Partial Differential Equations , 16 ( 2–3 ) : 451 – 489 .
  • Desvillettes , L. and Villani , C. 2001 . On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: the linear Fokker-Planck equation . Comm. Pure Appl. Math. , 54 ( 1 ) : 1 – 42 .
  • Desvillettes , L. and Villani , C. On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: nonlinear models . Preprint
  • Dolbeault , J. and Del Pino , M. 2002 . Best constants for Gagliardo-Nirenberg inequalities and application to nonlinear diffusions . J. Math. Pures Appl. , 81 ( 9 ) : 847 – 875 .
  • Fellner , K. , Neumann , L. and Schmeiser , C. Convergence to global equilibrium for spatially inhomogeneous kinetic models of non-micro-reversible processes . To appear in Monatsh. Math.
  • Grad , H. 1965 . On Boltzmann's H-Theorem . J. Soc. Indust. Appl. Math. , 13 : 259 – 277 .
  • Hérau , F. and Nier , F. 2002 . Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential . Preprint
  • Markowich , P. and Villani , C. On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis . Proceedings VI Workshop on Partial Differential Equations, Part II . 1999 , Rio de Janeiro. Vol. 19 , pp. 1 – 29 . Mat. Contemp.
  • Otto , F. 2001 . The geometry of dissipative evolution equations: the porous medium equation . Comm. Partial Differential Equations , 26 : 101 – 174 .
  • Villani , C. A review of mathematical topics in collisional kinetic theory Edited by: Friedlander , S. and Serre , D. Preprint, to appear in Handbook of Fluid Mechanics

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.