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

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Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

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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Authors and Affiliations

  1. Department of Mathematics and Research Center of Applied Mathematics, – (C.I.R.A.M.) – University of Bologna, Via Saragozza 8, I-40123 Bologna, Italy , , , , , , IT

    Guy Boillat & Tommaso Ruggeri

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  1. Guy Boillat
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  2. Tommaso Ruggeri
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Received February 15, 1998

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Boillat, G., Ruggeri, T. On the shock structure problem for hyperbolic system of balance laws and convex entropy. Continuum Mech Thermodyn 10, 285–292 (1998). https://doi.org/10.1007/s001610050094

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  • DOI: https://doi.org/10.1007/s001610050094

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