Geodesic
Shock wave acceleration in a gravitational field. Special case
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 61-64 
S. D. Kovalevskaya. Shock wave acceleration in a gravitational field. Special case. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 61-64. http://geodesic.mathdoc.fr/item/VMUMM_2016_1_a11/
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     author = {S. D. Kovalevskaya},
     title = {Shock wave acceleration in a gravitational field. {Special} case},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_1_a11/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The exact solution of the one-dimensional problem of shock wave acceleration in a uniform gravitational field at the state of equilibrium with a density that decreases according to a power low is given. The shock wave is generated by a piston moving freely in the gravitational field. The adiabatic index is equal to 3. The solution is represented in terms of elementary functions.

[1] Sedov L.I., Metody podobiya i razmernosti v mekhanike, 8-e izd., Nauka, M., 1977 | MR

[2] Chernyi G.G., Gazovaya dinamika, Nauka, M., 1988

[3] Golubyatnikov A.N., “O sfericheski-simmetrichnom dvizhenii gravitiruyuschego gaza pri nalichii silnoi udarnoi volny”, Dokl. AN SSSR, 227:5 (1976), 1067–1070

[4] Golubyatnikov A.N., Kovalevskaya S.D., “Avtomodelnye dvizheniya gaza v pole tyazhesti”, Izv. RAN. Mekhan. zhidkosti i gaza, 2014, no. 3, 123–132