Abstract
We consider a quasi-linear hyperbolic system in two independent variables (space and time), to evaluate the critical time for transmitted waves which arise when a discontinuity wave—travelling in a spherically symmetric medium—impacts with a shock wave generated by a «strong point explosion» within which the fluid is self-similar. The mass density in the ambient medium varies according to a power law of the radius, whereas the pressure is a very small fraction of that within the shock front. We proved that the critical time for the nonexceptional transmitted wave attains a finite value as the ambient pressure tends to zero, namely in the ideal case of complete validity of the self-similar solution.
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