An exponential formula for solving Boltzmann's equation for a Maxwellian gas

H. P. McKean

Research output: Contribution to journalArticle

Abstract

A class of nonlinear Boltzmann-like equations are interpreted from a probabilistic point of view. The model leads to an exponential formula for the solution, which, in the special cases considered, can be made explicit by algebraic and combinatorial considerations involving derivations of an associated algebra and exponentials of these and a (commutative but possibly nonassociative) multipliaction (convolution) on a dual of this algebra. Kac's idea of "propagation of chaos" plays a central role in all this.

Original languageEnglish (US)
Pages (from-to)358-382
Number of pages25
JournalJournal of Combinatorial Theory
Volume2
Issue number3
StatePublished - May 1967

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Boltzmann Equation
Propagation of Chaos
Algebra
Ludwig Boltzmann
Convolution
Gas
Model
Class

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An exponential formula for solving Boltzmann's equation for a Maxwellian gas. / McKean, H. P.

In: Journal of Combinatorial Theory, Vol. 2, No. 3, 05.1967, p. 358-382.

Research output: Contribution to journalArticle

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