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

This article is cited in 2 scientific papers (total in 2 papers)

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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\pages 232--265
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\jour Theoret. and Math. Phys.
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\pages 1614--1643
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  • http://mi.mathnet.ru/eng/tmf/v201/i2/p232

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. K. S. Platonova, A. V. Borovskikh, “Group analysis of the Boltzmann and Vlasov equations”, Theoret. and Math. Phys., 203:3 (2020), 794–823  mathnet  crossref  crossref  mathscinet  isi  elib
    2. K. S. Platonova, A. V. Borovskikh, “Group analysis of the one-dimensional Boltzmann equation. Invariants and the problem of moment system closure”, Theoret. and Math. Phys., 208:3 (2021), 1165–1181  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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