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

H. P. McKean

doi:10.1016/S0021-9800(67)80035-8

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

H. P. McKean

Mathematics

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

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 language	English (US)
Pages (from-to)	358-382
Number of pages	25
Journal	Journal of Combinatorial Theory
Volume	2
Issue number	3
DOIs	https://doi.org/10.1016/S0021-9800(67)80035-8
State	Published - May 1967

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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.",

author = "McKean, {H. P.}",

note = "Funding Information: * This work was completed at MIT, Cambridge, Mass., with the partial support of the National Science Foundation CNSF GP 4364), which is gratefully acknowledged.",

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AB - 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.

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

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