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On The Relative Entropy Method For Hyperbolic-Parabolic Systems

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Theory, Numerics and Applications of Hyperbolic Problems I (HYP 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 236))

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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.

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Acknowledgements

Christoforou would like to thank the organizers of XVI International Conference on Hyperbolic Problems Theory, Numerics, Applications (Hyp2016) that took place in Aachen from August 1st until 5th of 2016 for the invitation and the warm hospitality.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Cyprus, 1678, Nicosia, Cyprus

    Cleopatra Christoforou

  2. Computer, Electrical, Mathematical Sciences & Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia

    Athanasios Tzavaras

  3. Institute of Applied and Computational Mathematics, FORTH, Heraklion, Greece

    Athanasios Tzavaras

Authors
  1. Cleopatra Christoforou
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  2. Athanasios Tzavaras
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Corresponding author

Correspondence to Cleopatra Christoforou .

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Editors and Affiliations

  1. Department of Mathematics, WĂĽrzburg University, WĂĽrzburg, Germany

    Christian Klingenberg

  2. Department of Mathematics, RWTH Aachen University, Aachen, Germany

    Michael Westdickenberg

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Christoforou, C., Tzavaras, A. (2018). On The Relative Entropy Method For Hyperbolic-Parabolic Systems. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems I. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 236. Springer, Cham. https://doi.org/10.1007/978-3-319-91545-6_29

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