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JOURNALS // Ufimskii Matematicheskii Zhurnal // Archive

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

This article is cited 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.

UDC: 517.958+533.7

Received: 19.10.2012



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