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The Boltzmann kinetic equation and various models
Responsible organisation
2010 (English)In: Lecture Notes in Physics, ISSN 0075-8450, Vol. 806, 113-144 p.Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
Springer , 2010. Vol. 806, 113-144 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:bth-7597DOI: 10.1007/978-90-481-3797-8_3Local ID: oai:bth.se:forskinfo0A8BE537069EC57AC12578140033AC3COAI: oai:DiVA.org:bth-7597DiVA: diva2:835240
Available from: 2012-09-18 Created: 2011-01-10 Last updated: 2015-06-30Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
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Output format
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