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Ufimsk. Mat. Zh., 2013, Volume 5, Issue 1, Pages 125–129 (Mi ufa192)  

Reductions of partially invariant solutions of rank 1 defect 2 five-dimensional overalgebra of conical subalgebra

S. V. Khabirov

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

Abstract: Conic flows are the invariant rank 1 solutions of the gasdynamics equations on the three-dimensional subalgebra defined by the rotation operators, translation by time and uniform dilatation. The generalization of the conic flows are partially invariant solutions of rank 1 defect 2 on the five-dimensional overalgebra of conic subalgebra extended by the operators of space translations noncommuting with rotation. We prove that that the extensions of conic flows are reduced either to function-invariant plane stationary solutions or to a double wave of isobaric motions or to the simple wave.

Keywords: gas dynamics, conic flows, partially invariant solutions.

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English version:
Ufa Mathematical Journal, 2013, 5:1, 125–129 (PDF, 241 kB); https://doi.org/10.13108/2013-5-1-125

Bibliographic databases:

UDC: 517.3
Received: 10.01.2012

Citation: S. V. Khabirov, “Reductions of partially invariant solutions of rank 1 defect 2 five-dimensional overalgebra of conical subalgebra”, Ufimsk. Mat. Zh., 5:1 (2013), 125–129; Ufa Math. J., 5:1 (2013), 125–129

Citation in format AMSBIB
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\by S.~V.~Khabirov
\paper Reductions of partially invariant solutions of rank~1 defect~2 five-dimensional overalgebra of conical subalgebra
\jour Ufimsk. Mat. Zh.
\yr 2013
\vol 5
\issue 1
\pages 125--129
\mathnet{http://mi.mathnet.ru/ufa192}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3429956}
\elib{http://elibrary.ru/item.asp?id=18929632}
\transl
\jour Ufa Math. J.
\yr 2013
\vol 5
\issue 1
\pages 125--129
\crossref{https://doi.org/10.13108/2013-5-1-125}


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