In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.
@article{M2AN_2003__37_2_345_0,
author = {Desvillettes, Laurent and Salvarani, Francesco},
title = {Characterization of collision kernels},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {345--355},
publisher = {EDP-Sciences},
volume = {37},
number = {2},
year = {2003},
doi = {10.1051/m2an:2003030},
mrnumber = {1991205},
zbl = {1047.76114},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2003030/}
}
TY - JOUR AU - Desvillettes, Laurent AU - Salvarani, Francesco TI - Characterization of collision kernels JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 345 EP - 355 VL - 37 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003030/ DO - 10.1051/m2an:2003030 LA - en ID - M2AN_2003__37_2_345_0 ER -
%0 Journal Article %A Desvillettes, Laurent %A Salvarani, Francesco %T Characterization of collision kernels %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 345-355 %V 37 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003030/ %R 10.1051/m2an:2003030 %G en %F M2AN_2003__37_2_345_0
Desvillettes, Laurent; Salvarani, Francesco. Characterization of collision kernels. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 2, pp. 345-355. doi : 10.1051/m2an:2003030. http://www.numdam.org/articles/10.1051/m2an:2003030/
[1] ,, and, Entropy dissipation and long-range interactions. Arch. Ration. Mech. Anal. 152 (2000) 327-355. | Zbl
[2] and, On the Landau approximation in plasma physics. To appear in Ann. I.H.P. An. non linéaire. | Numdam | MR | Zbl
[3] , The Boltzmann equation and the group transformations. Math. Models Methods Appl. Sci. 3 (1993) 443-476. | Zbl
[4] , and, The mathematical theory of dilute gases. Springer Verlag, New York (1994). | MR | Zbl
[5] , Boltzmann's kernel and the spatially homogeneous Boltzmann equation. Riv. Mat. Univ. Parma 6 (2001) 1-22. | Zbl
[6] and, 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. | Zbl
[7] and, On the spatially homogeneous Landau equation for hard potentials. Part I: Existence, uniqueness and smoothness. Comm. Partial Differential Equations 25 (2000) 179-259. | Zbl
[8] , and, Asymptotic motion of a classical particle in a random potential in two dimensions: Landau model. Comm. Math. Phys. 113 (1987) 209-230. | Zbl
[9] , Rigorous theory of the Boltzmann equation in the Lorentz gas. Nota interna No. 358, Istituto di Fisica, Università di Roma (1973).
[10] and, Les distributions, Tome IV, Applications de l'analyse harmonique. Dunod, Paris (1967). | Zbl
[11] , The analysis of linear partial differential operators I. Springer Verlag, Berlin (1983). | Zbl
[12] and, Global validity of the Boltzmann equation for a two-dimensional rare gas in the vacuum. Comm. Math. Phys. 105 (1986) 189-203. | Zbl
[13] and, 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. | Zbl
[14] , Time evolution of large classical systems. Springer Verlag, Lecture Notes in Phys. 38 (1975) 1-111. | Zbl
[15] , A mathematical foundation for radiative transfer. J. Math. Mech. 6 (1957) 685-730. | Zbl
Cité par Sources :
