A Markov process associated with a Boltzmann equation without cutoff and for non-Maxwell molecules

Nicolas Fournier; Sylvie Méléard

doi:10.1023/A:1010322130480

A Markov process associated with a Boltzmann equation without cutoff and for non-Maxwell molecules

Nicolas Fournier
, Sylvie Méléard

IECN/UHP
Université Paris-Nanterre

Research output: Contribution to journal › Article › peer-review

Abstract

Tanaka,⁽¹⁸⁾ showed a way to relate the measure solution {P₁}₁ of a spatially homogeneous Boltzmann equation of Maxwellian molecules without angular cutoff to a Poisson-driven stochastic differential equation: {P₁} 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.

Original language	English
Pages (from-to)	359-385
Number of pages	27
Journal	Journal of Statistical Physics
Volume	104
Issue number	1-2
DOIs	https://doi.org/10.1023/A:1010322130480
Publication status	Published - 1 Jan 2001
Externally published	Yes

Keywords

Boltzmann equations without cutoff
Interacting particle systems
Jump measures
Nonlinear stochastic differential equations

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10.1023/A:1010322130480

Cite this

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abstract = "Tanaka,(18) showed a way to relate the measure solution \{P1\}1 of a spatially homogeneous Boltzmann equation of Maxwellian molecules without angular cutoff to a Poisson-driven stochastic differential equation: \{P1\} 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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N2 - Tanaka,(18) showed a way to relate the measure solution {P1}1 of a spatially homogeneous Boltzmann equation of Maxwellian molecules without angular cutoff to a Poisson-driven stochastic differential equation: {P1} 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.

AB - Tanaka,(18) showed a way to relate the measure solution {P1}1 of a spatially homogeneous Boltzmann equation of Maxwellian molecules without angular cutoff to a Poisson-driven stochastic differential equation: {P1} 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.

KW - Boltzmann equations without cutoff

KW - Interacting particle systems

KW - Jump measures

KW - Nonlinear stochastic differential equations

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1-2

ER -

A Markov process associated with a Boltzmann equation without cutoff and for non-Maxwell molecules

Abstract

Keywords

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