Shock Wave Acceleration in a Gravitational Field. A Special Case / S. D. Kovalevskaya. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 1. P. 61-64 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 16-18].

A one-dimensional problem of shock wave acceleration in a uniform gravitational field is exactly solved. In front of the shock wave, the medium state is initially in equilibrium and its density decreases according to a power law. The shock wave is generated using a piston moving freely in the gravitational field. The adiabatic index is assumed to be equal to 3. The obtained solution is represented in terms of elementary functions.

Key words: gravitational field, shock wave, acceleration.