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Sib. Èlektron. Mat. Izv., 2011, Volume 8, Pages 19–38 (Mi semr297)  

This article is cited in 6 scientific papers (total in 6 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

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.

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Document Type: Article
UDC: 517.958:533.7
MSC: 35B06, 35Q35
Received December 22, 2010, published January 16, 2011

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. V. Khabirov, “Nonisomorphic Lie algebras admitted by gasdynamic models”, Ufa Math. J., 3:2 (2011), 85–88  mathnet  zmath
    2. E. V. Makarevich, “Ierarkhiya podmodelei uravneniya gazovoi dinamiki s uravneniem sostoyaniya s razdelennoi plotnostyu”, Sib. elektron. matem. izv., 9 (2012), 306–328  mathnet
    3. L. Z. Urazbakhtina, “Integrable hydrodynamic submodels with a linear velocity field”, J. Appl. Industr. Math., 7:1 (2013), 117–126  mathnet  crossref  mathscinet
    4. E. V. Makarevich, “Kollaps ili mgnovennyi istochnik gaza na pryamoi”, Ufimsk. matem. zhurn., 4:4 (2012), 119–129  mathnet
    5. E. V. Makarevich, “Invariant and partially invariant solutions with respect to Galilean shifts and dilatation”, Ufa Math. J., 5:3 (2013), 118–126  mathnet  crossref  elib
    6. 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
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