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

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

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
Publisher	Springer Nature
Pages	363-374
Number of pages	12
ISBN (Print)	9783319915449
DOIs	https://doi.org/10.1007/978-3-319-91545-6_29
State	Published - Jun 23 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
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.

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

https://repository.kaust.edu.sa/bitstream/10754/628077/1/Christoforou-hyp2016.pdf

Cite this

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title = "On The Relative Entropy Method For Hyperbolic-Parabolic Systems",

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.",

author = "Cleopatra Christoforou and Athanasios Tzavaras",

note = "KAUST Repository Item: Exported on 2020-10-01 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.",

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

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AU - Tzavaras, Athanasios

N1 - KAUST Repository Item: Exported on 2020-10-01 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.

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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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SP - 363

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BT - Theory, Numerics and Applications of Hyperbolic Problems I

PB - Springer Nature

ER -

On The Relative Entropy Method For Hyperbolic-Parabolic Systems

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