Abstract
The dependences of the solutions to the hydrodynamic equations of compressed media that describe converging shock waves on the density of a substance ahead of a wave front are studied. The properties of Hugoniot adiabats that can explain the qualitatively different characters of these dependences for the equations of state of perfect gas and condensed matter are analyzed. The one-dimensional problems of converging shock waves in graphite and aluminum are considered, and the two-dimensional problem of the compression of graphite in a steel target with a conical cavity is solved. The latter problem is also investigated in terms of a simple model for a deformable solid that takes into account shear stresses.
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