On the Proof of Existence of Microscopic Solutions to the Boltzmann–Enskog Kinetic Equation

The problem of rigorous substantiation of the so-called microscopic solutions to the Boltzmann–Enskog kinetic equations discovered by N.N. Bogolyubov is considered. The solutions have the form of sums of delta functions and correspond to the reversible dynamics of a finite number of particles. Howev...

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Bibliographic Details
Published in:Physics of particles and nuclei 2020-07, Vol.51 (4), p.791-796
Main Author: Trushechkin, A. S.
Format: Article
Language:English
Subjects:
Particle and Nuclear Physics
Physics
Physics and Astronomy
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Summary:The problem of rigorous substantiation of the so-called microscopic solutions to the Boltzmann–Enskog kinetic equations discovered by N.N. Bogolyubov is considered. The solutions have the form of sums of delta functions and correspond to the reversible dynamics of a finite number of particles. However, the direct substitution of delta functions into the equation is formally incorrect. A regularization of the collision integral is proposed in this paper at which the substitution of delta functions becomes possible.
ISSN:1063-7796
1531-8559
DOI:10.1134/S1063779620040723