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 Sib. Èlektron. Mat. Izv., 2012, Volume 9, Pages 208–226 (Mi semr350)

Differentical equations, dynamical systems and optimal control

Submodels in gas dynamics with linear field of velocity

Yu. V. Yulmukhametova

Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences

Abstract: We consider the gas dynamics equation with an arbitrary state equation. After substitution of solution in the form of the linear field of velocity in equation of gas dynamics, the set of equations is received. Research of its compatibility gives a terminating parity into which the auxiliary matrix enters. This parity allowed to make classification of all submodels by a rank of an auxiliary matrix. All submodels for zero, degenerate and nondegenerate auxiliary matrixes are found. In separate point the case when the density depends only on time is considered. Quite certain submodel is found. It is as a result received quite certain 11 submodels of flow of gas with the linear field of velocity. For each submodel the equation of state is found.

Keywords: gas dynamics, line field of velocity, submodel.

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Document Type: Article
UDC: 517.958:532.5
MSC: 35Q35
Received January 23, 2012, published April 7, 2012

Citation: Yu. V. Yulmukhametova, “Submodels in gas dynamics with linear field of velocity”, Sib. Èlektron. Mat. Izv., 9 (2012), 208–226

Citation in format AMSBIB
\Bibitem{Yul12} \by Yu.~V.~Yulmukhametova \paper Submodels in gas dynamics with linear field of velocity \jour Sib. \Elektron. Mat. Izv. \yr 2012 \vol 9 \pages 208--226 \mathnet{http://mi.mathnet.ru/semr350} `