Geodesic
Shock wave acceleration in a gravitational field. Special case
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 61-64

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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. 
@article{VMUMM_2016_1_a11,
     author = {S. D. Kovalevskaya},
     title = {Shock wave acceleration in a gravitational field. {Special} case},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {61--64},
     publisher = {mathdoc},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_1_a11/}
}
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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/