The Boltzmann kinetic equation and various models

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Yurii Grigoriev, Nail H. Ibragimov, Vladimir Kovalev, Sergey Meleshko
Title: The Boltzmann kinetic equation and various models
Journal: Lecture Notes in Physics
Year: 2010
Volume: 806
Pagination: 113-144
ISSN: 0075-8450
Publisher: Springer
URI/DOI: 10.1007/978-90-481-3797-8_3
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. of Mathematics & Natural Sciences (Sektionen för ingenjörsvetenskap - Avd.för matematik och naturvetenskap)
School of Engineering S-371 79 Karlskrona
+46 455 38 50 00
Language: English
Abstract: The chapter deals with applications of the group analysis method to the full Boltzmann kinetic equation and some similar equations. These equations form the foundation of the kinetic theory of rarefied gas and coagulation. They typically include special integral operators with quadratic nonlinearity and multiple kernels which are called collision integrals. Calculations of the 11-parameter Lie group G 11 admitted by the full Boltzmann equation with arbitrary intermolecular potential and its extensions for power potentials are presented. The found isomorphism of these Lie groups with the Lie groups admitted by the ideal gas dynamics equations allowed one to obtain an optimal system of admitted subalgebras and to classify all invariant solutions of the full Boltzmann equation. For equations similar to the full Boltzmann equation complete admitted Lie groups are derived by solving determining equations. The corresponding optimal systems of admitted subalgebras are constructed and representations of all invariant solutions are obtained.
Subject: Mathematics\General