On the relative entropy method for hyperbolic-parabolic systems

Cleopatra Christoforou; Athanasios Tzavaras

doi:10.1007/978-3-319-91545-6_29

On the relative entropy method for hyperbolic-parabolic systems

Cleopatra Christoforou^*, Athanasios Tzavaras

^*Corresponding author for this work

Applied Mathematics and Computational Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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)
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	https://doi.org/10.1007/978-3-319-91545-6_29
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
Volume	236
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

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

Access to Document

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

Cite this

Christoforou, C., & Tzavaras, A. (2018). On the relative entropy method for hyperbolic-parabolic systems. In M. Westdickenberg, & C. Klingenberg (Eds.), Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016 (pp. 363-374). (Springer Proceedings in Mathematics and Statistics; Vol. 236). Springer New York LLC. https://doi.org/10.1007/978-3-319-91545-6_29

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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.",

keywords = "Conservation laws, Convergence, Dissipative measure-valued, Hyperbolic-parabolic, Relative entropy, Weak solutions, Weak-strong uniqueness",

author = "Cleopatra Christoforou and Athanasios Tzavaras",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.; 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 ; Conference date: 01-08-2016 Through 05-08-2016",

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doi = "10.1007/978-3-319-91545-6_29",

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Christoforou, C & Tzavaras, A 2018, On the relative entropy method for hyperbolic-parabolic systems. in M Westdickenberg & C Klingenberg (eds), Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016. Springer Proceedings in Mathematics and Statistics, vol. 236, Springer New York LLC, pp. 363-374, 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016, Aachen, Germany, 08/1/16. https://doi.org/10.1007/978-3-319-91545-6_29

On the relative entropy method for hyperbolic-parabolic systems. / Christoforou, Cleopatra; Tzavaras, Athanasios.
Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016. ed. / Michael Westdickenberg; Christian Klingenberg. Springer New York LLC, 2018. p. 363-374 (Springer Proceedings in Mathematics and Statistics; Vol. 236).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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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.

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KW - Convergence

KW - Dissipative measure-valued

KW - Hyperbolic-parabolic

KW - Relative entropy

KW - Weak solutions

KW - Weak-strong uniqueness

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On the relative entropy method for hyperbolic-parabolic systems

Abstract

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Bibliographical note

Keywords

ASJC Scopus subject areas

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