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

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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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
2. E. V. Makarevich, “Ierarkhiya podmodelei uravneniya gazovoi dinamiki s uravneniem sostoyaniya s razdelennoi plotnostyu”, Sib. elektron. matem. izv., 9 (2012), 306–328
3. L. Z. Urazbakhtina, “Integrable hydrodynamic submodels with a linear velocity field”, J. Appl. Industr. Math., 7:1 (2013), 117–126
4. E. V. Makarevich, “Kollaps ili mgnovennyi istochnik gaza na pryamoi”, Ufimsk. matem. zhurn., 4:4 (2012), 119–129
5. E. V. Makarevich, “Invariant and partially invariant solutions with respect to Galilean shifts and dilatation”, Ufa Math. J., 5:3 (2013), 118–126
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
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