On the shock structure problem for hyperbolic system of balance laws and convex entropy

In this paper we give a brief survey of the problem of shock structure solutions in fluid dynamics. For a generic system of balance laws compatible with an entropy principle and a convex entropy we prove that $C^1$ solutions cannot exist when the shock velocity exceeds the maximum characteristic velocity in the equilibrium state in front of the shock. This is in agreement with a conjecture of Extended Thermodynamics.

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