Free access
Issue
ESAIM: M2AN
Volume 37, Number 2, March/April 2003
Page(s) 345 - 355
DOI http://dx.doi.org/10.1051/m2an:2003030
Published online 15 November 2003
  1. R. Alexandre, L. Desvillettes, C. Villani and B. Wennberg, Entropy dissipation and long-range interactions. Arch. Ration. Mech. Anal. 152 (2000) 327-355. [CrossRef] [MathSciNet]
  2. R. Alexandre and C. Villani, On the Landau approximation in plasma physics. To appear in Ann. I.H.P. An. non linéaire.
  3. A.V. Bobylev, The Boltzmann equation and the group transformations. Math. Models Methods Appl. Sci. 3 (1993) 443-476. [CrossRef] [MathSciNet]
  4. C. Cercignani, R. Illner and M. Pulvirenti, The mathematical theory of dilute gases. Springer Verlag, New York (1994).
  5. L. Desvillettes, Boltzmann's kernel and the spatially homogeneous Boltzmann equation. Riv. Mat. Univ. Parma 6 (2001) 1-22.
  6. L. Desvillettes and V. Ricci, A rigorous derivation of a linear kinetic equation of Fokker-Planck type in the limit of grazing collisions. J. Statist. Phys. 104 (2001) 1173-1189. [CrossRef] [MathSciNet]
  7. L. Desvillettes and C. Villani, On the spatially homogeneous Landau equation for hard potentials. Part I: Existence, uniqueness and smoothness. Comm. Partial Differential Equations 25 (2000) 179-259. [CrossRef] [MathSciNet]
  8. D. Dürr, S. Goldstein and J. Lebowitz, Asymptotic motion of a classical particle in a random potential in two dimensions: Landau model. Comm. Math. Phys. 113 (1987) 209-230. [CrossRef] [MathSciNet]
  9. G. Gallavotti, Rigorous theory of the Boltzmann equation in the Lorentz gas. Nota interna No. 358, Istituto di Fisica, Università di Roma (1973).
  10. I.M. Guelfand and N.Y. Vilenkin, Les distributions, Tome IV, Applications de l'analyse harmonique. Dunod, Paris (1967).
  11. L. Hörmander, The analysis of linear partial differential operators I. Springer Verlag, Berlin (1983).
  12. R. Illner and M. Pulvirenti, Global validity of the Boltzmann equation for a two-dimensional rare gas in the vacuum. Comm. Math. Phys. 105 (1986) 189-203. [CrossRef] [MathSciNet]
  13. R. Illner and M. Pulvirenti, Global validity of the Boltzmann equation for two- and three-dimensional rare gas in the vacuum: erratum and improved result. Comm. Math. Phys. 121 (1989) 143-146. [CrossRef] [MathSciNet]
  14. O. Lanford, Time evolution of large classical systems. Springer Verlag, Lecture Notes in Phys. 38 (1975) 1-111.
  15. R.W. Preisendorfer, A mathematical foundation for radiative transfer. J. Math. Mech. 6 (1957) 685-730. [MathSciNet]

Recommended for you