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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 4, Pages 119–129 (Mi ufa173)  

This article is cited in 1 scientific paper (total in 1 paper)

The collapse or the source of gas on a straight line

E. V. Makarevich

Ufa State Aviation Technical University, Ufa, Russia

Abstract: In the work the partially invariant solution of the rank 2 defect 0 on four-dimensional subalgebra is constructed. The motion of allocated volume of gas is described. The motion of sound surface is constructed, where the velocity of particles is equal to sound velocity. The motion of the sound characteristics and conoid is described. The solution specifies gas motion from the whole space towards the straight line for negative time (collapse) and from the line to the whole space for positive time (source). For infinitely large absolute time values the motion is subsonic everywhere. The sound surface moves from infinitely distant points towards the straight line. It is shown, that the sound characteristics and conoid points move towards the sound surface.

Keywords: gas dynamics, partially invariant solution, collapse, conoid.

Full text: PDF file (427 kB)
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UDC: 517.958+533.7
Received: 19.10.2012

Citation: E. V. Makarevich, “The collapse or the source of gas on a straight line”, Ufimsk. Mat. Zh., 4:4 (2012), 119–129

Citation in format AMSBIB
\Bibitem{Mak12}
\by E.~V.~Makarevich
\paper The collapse or the source of gas on a~straight line
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 4
\pages 119--129
\mathnet{http://mi.mathnet.ru/ufa173}


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  • http://mi.mathnet.ru/eng/ufa/v4/i4/p119

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. V. Makarevich, “Invariant and partially invariant solutions with respect to Galilean shifts and dilatation”, Ufa Math. J., 5:3 (2013), 118–126  mathnet  crossref  elib
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