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 Chelyab. Fiz.-Mat. Zh., 2018, Volume 3, Issue 1, Pages 38–57 (Mi chfmj90)

Mathematics

Invariant submodel of rank 2 on subalgebra of translations linear combinations for a hydrodynamic type model

D. T. Siraevaa, S. V. Khabirovb

a Ufa State Aviation Technical University, Ufa, Russia
b Mavlutov Institute of Mechanics of Ufa Scientific Center of RAS, Ufa, Russia

Abstract: The equations of hydrodynamic type with the equation of state in the form of pressure, represented as a sum of density and entropy functions, are considered in the article. For the invariant submodel of a 2-dimensional subalgebra in the form of a linear combination of translations chosen from the previously constructed optimal system of non-similar subalgebras, we find the integrals of the system, determine the type of the system, reduce the system to the symmetric form and the characteristic form, find exact solutions, define equivalence transformations for the linearized system, the group classification problem is solved, an optimal system of non-similar subalgebras is constructed, and the application of integral transformations is shown.

Keywords: subalgebra, invariant submodel, exact solution, group classification, equivalence transformation.

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UDC: 517.95
Revised: 15.02.2018

Citation: D. T. Siraeva, S. V. Khabirov, “Invariant submodel of rank 2 on subalgebra of translations linear combinations for a hydrodynamic type model”, Chelyab. Fiz.-Mat. Zh., 3:1 (2018), 38–57

Citation in format AMSBIB
\Bibitem{SirKha18} \by D.~T.~Siraeva, S.~V.~Khabirov \paper Invariant submodel of rank 2 on subalgebra of translations linear combinations for a hydrodynamic type model \jour Chelyab. Fiz.-Mat. Zh. \yr 2018 \vol 3 \issue 1 \pages 38--57 \mathnet{http://mi.mathnet.ru/chfmj90} \elib{https://elibrary.ru/item.asp?id=32485877} 

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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. D. T. Siraeva, “Klassifikatsiya statsionarnykh podmodelei ranga 2 idealnoi gidrodinamiki”, Chelyab. fiz.-matem. zhurn., 4:1 (2019), 18–32
2. D. T. Siraeva, “The canonical form of the rank 2 invariant submodels of evolutionary type in ideal hydrodynamics”, J. Appl. Industr. Math., 13:2 (2019), 340–349
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