Kinetic and Related Models (KRM)

Particle approximation of some Landau equations

Pages: 451 - 464, Volume 2, Issue 3, September 2009      doi:10.3934/krm.2009.2.451

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Nicolas Fournier - LAMA UMR 8050, Faculté de Sciences et Technologies, Université Paris Est, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France (email)

Abstract: We consider a class of nonlinear partial-differential equations, including the spatially homogeneous Fokker-Planck-Landau equation for Maxwell (or pseudo-Maxwell) molecules. Continuing the work of [6, 7, 4], we propose a probabilistic interpretation of such a P.D.E. in terms of a nonlinear stochastic differential equation driven by a standard Brownian motion. We derive a numerical scheme, based on a system of $n$ particles driven by $n$ Brownian motions, and study its rate of convergence. We finally deal with the possible extension of our numerical scheme to the case of the Landau equation for soft potentials, and give some numerical results.

Keywords:  Fokker-Planck-Landau equation, Plasma physics, Stochastic particle systems.
Mathematics Subject Classification:  82C40, 60K35.

Received: February 2009;      Revised: June 2009;      Available Online: July 2009.