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We solve the continuation problem for the non-isentropic Euler equations following the collapse of an imploding shock wave. More precisely, we prove that the self-similar G\"uderley imploding shock solutions for a perfect gas with adiabatic exponent (1, 3] admit a self-similar extension consisting of two regions of smooth flow separated by an outgoing spherically symmetric shock wave of finite strength. In addition, for (1, 53], we show that there is a unique choice of shock wave that gives rise to a globally defined self-similar flow with physical state at the spatial origin.
Jang et al. (Mon,) studied this question.
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