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The Boltzmann kinetic equation and various models
Ansvarlig organisasjon
2010 (engelsk)Inngår i: Lecture Notes in Physics, ISSN 0075-8450, Vol. 806, s. 113-144Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

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.

sted, utgiver, år, opplag, sider
Springer , 2010. Vol. 806, s. 113-144
HSV kategori
Identifikatorer
URN: urn:nbn:se:bth-7597DOI: 10.1007/978-90-481-3797-8_3Lokal ID: oai:bth.se:forskinfo0A8BE537069EC57AC12578140033AC3COAI: oai:DiVA.org:bth-7597DiVA, id: diva2:835240
Tilgjengelig fra: 2012-09-18 Laget: 2011-01-10 Sist oppdatert: 2015-06-30bibliografisk kontrollert

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