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 http://www.bth.se/ing/ |
| 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 |
