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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 585–602 (Mi semr938)  

Differentical equations, dynamical systems and optimal control

Invariant submodels of system equations of two-velocity hydrodynamics with equilibrium of pressure phases

G. S. Vasilieva, Jian-Gang Tangb, B. Zh. Mamasolievc

a Institute of Computational Mathematics and Mathematical Geophysics, pr. Lavrentieva, 6, 630090, Novosibirsk, Russia
b YiLi Normal University, Jiefang Road, 448, 835000, Yinning Xinjiang, P.R. of China
c National University of Uzbekistan named after Mirzo Ulugbek, Universitet Ko'chasi, 4, 100174, Tashkent, Uzbekistan

Abstract: We found the main core of Lie groups of transformations for a one-dimensional system of two-velocity hydrodynamic equations with equilibrium of pressure phases, using the theory of Lie groups and Lie algebra. Also, all systems of differential equations for invariant and partially invariant solutions for all non-subgroups, algebras that are included in optimal systems are written out. In some cases, solutions have been found.

Keywords: two-velocity hydrodynamic, Lie algebra, invariant solution.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-51-41002
18-41-540010
16-01-00729_а


DOI: https://doi.org/10.17377/semi.2018.15.047

Full text: PDF file (210 kB)
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Bibliographic databases:

Document Type: Article
UDC: 512.812.4
MSC: 17B81
Received June 17, 2016, published May 17, 2018

Citation: G. S. Vasiliev, Jian-Gang Tang, B. Zh. Mamasoliev, “Invariant submodels of system equations of two-velocity hydrodynamics with equilibrium of pressure phases”, Sib. Èlektron. Mat. Izv., 15 (2018), 585–602

Citation in format AMSBIB
\Bibitem{VasTanMam18}
\by G.~S.~Vasiliev, Jian-Gang~Tang, B.~Zh.~Mamasoliev
\paper Invariant submodels of system equations of two-velocity hydrodynamics with equilibrium of pressure phases
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 585--602
\mathnet{http://mi.mathnet.ru/semr938}
\crossref{https://doi.org/10.17377/semi.2018.15.047}


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