Abstract
New exact solutions of the equation of one-dimensional gas dynamics with strong shock waves propagating in a moving medium are obtained. The gas flow behind a discontinuity is described by a solution with uniform deformation (see /1, 2/). Solutions of the explosion problem without a counterpressure in a uniformly expanding (or compressing) gas with an arbitrary adiabatic exponent and a non-uniform initial density distribution are constructed, as well as of the problem of cavity collapse in a dust cloud with the formation of a shock wave. The solution (see /1, 2/) was joined with the shock and detonation waves propagating in a quiescent gas in /3 – 6/. The problem of joining, by the use of the shock wave, of a solution for a moving selfgravitating medium with zero pressure, and the problem of selfsimilar solutions were discussed in /7/. An exact solution of the problem of a strong explosion in a uniformly expanding (or compressing) gas with a special adiabatic exponent equal to 5/3 was obtained in /8/.
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