Exact solutions of problems about optimum compression of gas by cylindrical and spherical shock waves

The simple analytical solutions have been derived for the cylindrical and spherical converging shock waves in the ideal gas. The similar problems had already been solved by Guderley (Guderley, Luftgahrtforschung 19 (1943) 3; Landau and Stanukovich, 1955), but that solution is obtained for the situation with the initial push (piston), which the piston is located at the distance very far from the center, therefore the initial push does not influence on the final stages of cumulating. Such Problems (Guderleyʹs problem) can be solved by numerical methods only. Here in our cases the piston drives a shock wave front to the center at the critical moment of cumulating, and the particular simple analytical solutions may be derived. The corrugation stability of shock wave fronts has been investigated also.