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JOURNALS // Ufimskii Matematicheskii Zhurnal // Archive

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

This article is cited in 1 paper

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.

UDC: 517.3

Received: 10.01.2012


 English version:
Ufa Mathematical Journal, 2013, 5:1, 125–129

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