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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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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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\jour Ufa Math. J.
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http://mi.mathnet.ru/eng/ufa192 http://mi.mathnet.ru/eng/ufa/v5/i1/p125
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