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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2011, Volume 8, Pages 19–38 (Mi semr297)  

This article is cited in 7 scientific papers (total in 7 papers)

Research papers

Optimal system of subalgebras admitted by the gas dynamics equations in case of state equation with separated density

E. V. Makarevich

Ufa State Aviation Technical University
Full-text PDF (776 kB) Citations (7)
References:
Abstract: We consider the gas dynamics equations with the state equation of separated density. The optimal system of subalgebras for a $12$-dimensional Lie algebra admitted by the gas dynamics equations is given. We use the decomposition of a $12$-dimensional Lie algebra to the semidirect sum of a $6$-dimensional Abelian ideal and a $6$-dimensional subalgebra to construct the optimal system. On the first step we construct the optimal system of projections on $6$ dimensional subalgebra. Then the projections are complemented with elements from Abelian ideal. We propose the compact notation of the optimal system of subalgebras for $12$-dimensional Lie algebra which is constructed with the help of the optimal system for $6$-dimensional subalgebra.
Keywords: optimal system of subalgebras, gas dynamics equations, state equation of the separated density.
Received December 22, 2010, published January 16, 2011
Document Type: Article
UDC: 517.958:533.7
MSC: 35B06, 35Q35
Language: Russian
Citation: E. V. Makarevich, “Optimal system of subalgebras admitted by the gas dynamics equations in case of state equation with separated density”, Sib. Èlektron. Mat. Izv., 8 (2011), 19–38
Citation in format AMSBIB
\Bibitem{Mak11}
\by E.~V.~Makarevich
\paper Optimal system of subalgebras admitted by the gas dynamics equations in case of state equation with separated density
\jour Sib. \`Elektron. Mat. Izv.
\yr 2011
\vol 8
\pages 19--38
\mathnet{http://mi.mathnet.ru/semr297}
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  • https://www.mathnet.ru/eng/semr/v8/p19
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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