TY - GEN

T1 - On the relative entropy method for hyperbolic-parabolic systems

AU - Christoforou, Cleopatra

AU - Tzavaras, Athanasios

N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Conservation laws

KW - Convergence

KW - Dissipative measure-valued

KW - Hyperbolic-parabolic

KW - Relative entropy

KW - Weak solutions

KW - Weak-strong uniqueness

UR - http://www.scopus.com/inward/record.url?scp=85049375774&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-91545-6_29

DO - 10.1007/978-3-319-91545-6_29

M3 - Conference contribution

AN - SCOPUS:85049375774

SN - 9783319915449

T3 - Springer Proceedings in Mathematics and Statistics

SP - 363

EP - 374

BT - Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016

A2 - Westdickenberg, Michael

A2 - Klingenberg, Christian

PB - Springer New York LLC

T2 - 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016

Y2 - 1 August 2016 through 5 August 2016

ER -