Derivation of a Nonautonomous Linear Boltzmann Equation from a Heterogeneous Rayleigh Gas

Karsten Matthies; George Stone

doi:10.3934/dcds.2018143

Derivation of a Nonautonomous Linear Boltzmann Equation from a Heterogeneous Rayleigh Gas

Karsten Matthies, George Stone

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Abstract

A linear Boltzmann equation with non-autonomous collision operator is rigorously derived in the Boltzmann-Grad limit for the deterministic dynamics of a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with heterogeneously distributed background particles, which do not interact among each other. The validity of the linear Boltzmann equation holds for arbitrary long times under moderate assumptions on spatial continuity and higher moments of the initial distributions of the tagged particle and the heterogeneous, non-equilibrium distribution of the background. The empiric particle dynamics are compared to the Boltzmann dynamics using evolution systems for Kolmogorov equations of associated probability measures on collision histories.

Original language	English
Pages (from-to)	3299-3355
Number of pages	57
Journal	Discrete and Continuous Dynamical Systems - Series A
Volume	38
Issue number	7
DOIs	https://doi.org/10.3934/dcds.2018143
Publication status	Published - 1 Jul 2018

Keywords

Boltzmann equation
Derivation
Evolution system
Rayleigh gas.
Semigroup

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2018143

HetRayleigh
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Dynamical Systems following peer review. The definitive publisher-authenticated version Matthies, K & Stone, G 2018, 'Derivation of a Nonautonomous Linear Boltzmann Equation from a Heterogeneous Rayleigh Gas' Discrete and Continuous Dynamical Systems - Series A, vol 38, no. 7, pp. 3299-3355 is available online at: http://dx.doi.org/10.3934/dcds.2018143.
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Cite this

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Derivation of a Nonautonomous Linear Boltzmann Equation from a Heterogeneous Rayleigh Gas

Abstract

Keywords

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