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 Ufimsk. Mat. Zh., 2012, Volume 4, Issue 4, Pages 147–154 (Mi ufa176)

Extention of the conic flows

S. V. Khabirovab

a Ufa State Aviation Technical University, Ufa, Russia
b Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences, Ufa, Russia

Abstract: All partial invariant solutions of gas dynamic equations constructed on the conic subalgebra admitted by the model are found. The canonic subalgebra consists of operators of rotation, translation by time and expansion. Submodel is set by a system of ordinary differential equations. Solutions form a series of submodels. In the basis of this submodels lies canonic submodel with respect to the invariant variable depending on independent variables and constants of this submodels depending on the invariant function. To determine this dependence, various additional overdetermined equations are obtained. Moreover, two submodels, expanding the canonic submodel, are derived from the system of partial differential equations. All formulas returning the solutions to physical space are defined for these two submodels.

Keywords: canonic flows, partial invariant solutions, gas dynamics.

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UDC: 517.9

Citation: S. V. Khabirov, “Extention of the conic flows”, Ufimsk. Mat. Zh., 4:4 (2012), 147–154

Citation in format AMSBIB
\Bibitem{Kha12} \by S.~V.~Khabirov \paper Extention of the conic flows \jour Ufimsk. Mat. Zh. \yr 2012 \vol 4 \issue 4 \pages 147--154 \mathnet{http://mi.mathnet.ru/ufa176}