## Abstract

The work of Christoforou and Tzavaras (Arch Rat Mech Anal 229(1):1–52, 2018, [5]) on the extension of the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable is the context of this article. The general theory is presented and the derivation of the relative entropy identities for both hyperbolic and hyperbolic-parabolic systems is presented. The resulting identities are useful to provide measure valued weak versus strong uniqueness theorems as well as convergence results in the zero-viscosity limit. An application of this theory is given for the example of the system of thermoviscoelasticity.

Original language | English (US) |
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Title of host publication | Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016 |

Editors | Michael Westdickenberg, Christian Klingenberg |

Publisher | Springer New York LLC |

Pages | 363-374 |

Number of pages | 12 |

ISBN (Print) | 9783319915449 |

DOIs | |

State | Published - 2018 |

Event | 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 - Aachen, Germany Duration: Aug 1 2016 → Aug 5 2016 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 236 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 |
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Country/Territory | Germany |

City | Aachen |

Period | 08/1/16 → 08/5/16 |

### Bibliographical note

Publisher Copyright:© Springer International Publishing AG, part of Springer Nature 2018.

## Keywords

- Conservation laws
- Convergence
- Dissipative measure-valued
- Hyperbolic-parabolic
- Relative entropy
- Weak solutions
- Weak-strong uniqueness

## ASJC Scopus subject areas

- General Mathematics