DC MetaData pour: Monte-Carlo approximations for 2d homogeneous Boltzmann equations without cutoff and for non Maxwell molecules


Université Paris 6 Pierre et Marie Curie		Université Paris 7 Denis Diderot

	CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Monte-Carlo approximations for 2d homogeneous Boltzmann equations without cutoff and for non Maxwell molecules

Auteur(s):

N. FOURNIER

S. MÉLÉARD

Code(s) de Classification MSC:

60H30 Applications of stochastic analysis (to PDE, etc.)
60K35 Interacting random processes; statistical mechanics type models; percolation theory, See also {82B43, 82C43}
82C40 Kinetic theory of gases

Résumé: In [10], using a typically probabilistic substitution in the Boltzmann equation, we extend Tanaka's probabilistic interpretation [19] to much more general spatially homogeneous Boltzmann equations, i.e. homogeneous Boltzmann equations without cutoff and for non Maxwell molecules. In this paper we show how this interpretation allows us to build some approximating cutoff interacting particle systems, and to derive some Monte-Carlo algorithms for the simulation of solutions of the Boltzmann equation.

Mots Clés: Boltzmann equations without cutoff and for non Maxwell molecules ; Nonlinear stochastic differential equations ; Interacting particle systems ; Monte-Carlo algorithm

Date: 2000-12-13

Prépublication numéro: PMA-630

Postscript file : PMA-630.ps