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TMF, 2019, Volume 201, Number 2, Pages 232–265 (Mi tmf9708)  

Group analysis of the one-dimensional Boltzmann equation: IV. Complete group classification in the general case

A. V. Borovskikh, K. S. Platonova

Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider the one-dimensional Boltzmann equation $f_t+cf_x+(\mathcal{F} f)_c=0$ with a function $\mathcal{F}$ depending on $(t,x,c,f)$ and obtain the complete group classification of such equations in the class of point changes of whole set of variables $(t,x,c,f)$. For this, we impose additional conditions on the transformations for the invariance of (a) the relations $dx=c dt$ and $dc=\mathcal{F} dt$, (b) the lines $dt=dx=0$, and (c) the form $f dx dc$, which fix the physical meaning of the used variables and the relations between them.

Keywords: Boltzmann equation, symmetry group, equivalence group, gas dynamics equation.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf9708

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English version:
Theoretical and Mathematical Physics, 2019, 201:2, 1614–1643

Bibliographic databases:

MSC: 35Q20
Received: 25.02.2019
Revised: 24.05.2019

Citation: A. V. Borovskikh, K. S. Platonova, “Group analysis of the one-dimensional Boltzmann equation: IV. Complete group classification in the general case”, TMF, 201:2 (2019), 232–265; Theoret. and Math. Phys., 201:2 (2019), 1614–1643

Citation in format AMSBIB
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\by A.~V.~Borovskikh, K.~S.~Platonova
\paper Group analysis of the~one-dimensional Boltzmann equation: IV.~Complete group classification in the~general case
\jour TMF
\yr 2019
\vol 201
\issue 2
\pages 232--265
\mathnet{http://mi.mathnet.ru/tmf9708}
\crossref{https://doi.org/10.4213/tmf9708}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2019TMP...201.1614B}
\transl
\jour Theoret. and Math. Phys.
\yr 2019
\vol 201
\issue 2
\pages 1614--1643
\crossref{https://doi.org/10.1134/S0040577919110072}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85076345400}


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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