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Interaction of a singular surface with a strong shock in the interstellar gas clouds. (English) Zbl 1482.76073

This paper considers the system of partial differential equations modelling the self-gravitating interstellar gas clouds in spherical symmetry. Using the Lie group of transformations, the governing system of partial differential equations reduces to a system of ordinary differential equations for obtaining self-similar solutions. The key idea of this paper is to investigate the results of the interaction between a singular surface and a strong shock in the self-gravitating spherically symmetric interstellar gas clouds. It is proved that there are no transmitted waves, and hence the amplitudes of reflected waves are obtained, which are directly proportional to the amplitude of the jump in velocity gradient.

MSC:

76L05 Shock waves and blast waves in fluid mechanics
76N15 Gas dynamics (general theory)
76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
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