A Markov Process Associated with a Boltzmann Equation Without Cutoff and for Non-Maxwell Molecules |
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| Authors: | Nicolas Fournier Sylvie Méléard |
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| Institution: | (1) Campus Scientifique, Institut Elie Cartan, BP 239, 54506 Vandoeuvre-lès-Nancy Cedex, France;(2) Université Paris 10, MODALX, 200 av. de la République, 92000 Nanterre;(3) ASCI (UPR 9029), Bat. 506, Université Paris Sud, 91405 Orsay cedex, France |
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| Abstract: | Tanaka,(18) showed a way to relate the measure solution {P
t
}
t
of a spatially homogeneous Boltzmann equation of Maxwellian molecules without angular cutoff to a Poisson-driven stochastic differential equation: {P
t
} is the flow of time marginals of the solution of this stochastic equation. In the present paper, we extend this probabilistic interpretation to much more general spatially homogeneous Boltzmann equations. Then we derive from this interpretation a numerical method for the concerned Boltzmann equations, by using easily simulable interacting particle systems. |
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| Keywords: | Boltzmann equations without cutoff nonlinear stochastic differential equations jump measures interacting particle systems |
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