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Ufimsk. Mat. Zh., 2011, Volume 3, Issue 2, Pages 87–90 (Mi ufa96)  

This article is cited in 4 scientific papers (total in 4 papers)

Nonisomorphic Lie algebras admitted by gasdynamic models

S. V. Khabirov

Institute of Mechanics, Ufa Science Centre of Russian Academy of Sciences, Ufa, Russia

Abstract: Group classification of gasdynamic equations by the state equation consists of 13 types of finite-dimensional Lie algebras of different dimensions, from 11 to 14. Some types depend on a parameter. Five pairs of Lie algebras appear to be equivalent. The equivalent transformations for Lie algebras contain the equivalent transformations for gasdynamic equations. The equivalence test resulted in nine nonisomorphic Lie algebras with different structures. One type has 3 different structures for different parameters. Each of these Lie algebras is represented as a semidirect sum of a six-dimensional Abeilian ideal with a subalgebra, which is decomposed into a semidirect or direct sum in its turn. The optimal systems for subalgebras are constructed. The Abeilian ideal is added in 6 cases while constructing the optimal system. There remain 3 Lie algebras of the dimensions 12, 13, 14 for which the optimal systems are not constructed.

Keywords: gas dynamics, Lie algebra, equivalent transformation, optimal system.

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English version:
Ufa Mathematical Journal, 2011, 3:2, 85–88 (PDF, 256 kB)

Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 25.03.2011

Citation: S. V. Khabirov, “Nonisomorphic Lie algebras admitted by gasdynamic models”, Ufimsk. Mat. Zh., 3:2 (2011), 87–90; Ufa Math. J., 3:2 (2011), 85–88

Citation in format AMSBIB
\Bibitem{Kha11}
\by S.~V.~Khabirov
\paper Nonisomorphic Lie algebras admitted by gasdynamic models
\jour Ufimsk. Mat. Zh.
\yr 2011
\vol 3
\issue 2
\pages 87--90
\mathnet{http://mi.mathnet.ru/ufa96}
\zmath{https://zbmath.org/?q=an:1249.76076}
\transl
\jour Ufa Math. J.
\yr 2011
\vol 3
\issue 2
\pages 85--88


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    This publication is cited in the following articles:
    1. A. M. Ilyasov, “Optimal system of Lie algebra subalgebras of the point symmetries group for nonlinear heat equation without source”, Ufa Math. J., 5:3 (2013), 53–66  mathnet  crossref  elib
    2. D. T. Siraeva, “Optimal system of non-similar subalgebras of sum of two ideals”, Ufa Math. J., 6:1 (2014), 90–103  mathnet  crossref  isi  elib
    3. S. V. Khabirov, “Optimal system for the sum of two ideals admitted by the hydrodynamic type equations”, Ufa Math. J., 6:2 (2014), 97–101  mathnet  crossref  elib
    4. D. T. Siraeva, S. V. Khabirov, “Invariantnaya podmodel ranga 2 na podalgebre iz lineinoi kombinatsii perenosov dlya modeli gidrodinamicheskogo tipa”, Chelyab. fiz.-matem. zhurn., 3:1 (2018), 38–57  mathnet  elib
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