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 -