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Optimal system for the sum of two ideals admitted by the hydrodynamic type equations. (Russian. English summary) Zbl 1374.76189

In the known article of L. V. Ovsyannikov [J. Appl. Math. Mech. 58, No. 4, 601–627 (1994); translation from Prikl. Mat. Mekh. 58, No. 4, 30–55 (1994; Zbl 0890.76070)] the SUBMODELS program is introduced with its main problems: computation of admitted Lie group; group classification on the equation of the state; construction of optimal system of subalgebras for models of the group classification; study of submodels constructed on subalgebras. In the author’s article [Ufim. Mat. Zh. 3, No. 2, 87–90 (2011; Zbl 1249.76076)] it is shown that for models of hydrodynamic type there are ten non-isomorphic finite dimensional Lie algebras. For almost all of them optimal subalgebras systems are constructed.
It is needed to construct optimal system of subalgebras for five Lie algebras of the sum of two ideals for which optimal systems are already constructed. This problem is solved in the article under review.

MSC:

76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
35A30 Geometric theory, characteristics, transformations in context of PDEs
35Q35 PDEs in connection with fluid mechanics
76N15 Gas dynamics (general theory)
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References:

[1] Ovsyannikov L. V., “Programma podmodeli. Gazovaya dinamika”, Prikladnaya matematika i mekhanika, 58:4 (1994), 30-55 · Zbl 0890.76070
[2] Khabirov S. V., “Neizomorfnye algebry Li, dopuskaemye modelyami gazovoi dinamiki”, Ufimskii matematicheskii zhurnal, 3:2 (2011), 87-90 · Zbl 1249.76076
[3] Makarevich E. V., “Opimalnaya sistema podalgebr, dopuskaemykh uravneniyami gazovoi dinamiki v sluchae uravnenii sostoyaniya s razdelennoi plotnostyu”, Sibirskie elektronnye matematicheskie izvestiya, 8 (2011), 19-38 · Zbl 1329.76299
[4] Siraeva D. T., “Opimalnaya sistema 11-mernoi algebry Li, rasshirennoi kommutiruyuschim operatorom”, Ufimskii matematicheskii zhurnal, 6:1 (2014), 94-107 · Zbl 1299.35018
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