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Review

Recent Advances on Boundary Conditions for Equations in Nonequilibrium Thermodynamics

by 1,2,* and 3
1
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
2
Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China
3
School of Mathematical Sciences, Peking University, Beijing 100871, China
*
Author to whom correspondence should be addressed.
Academic Editors: Róbert Kovács, Patrizia Rogolino, Francesco Oliveri, Charles F. Dunklm, Marin Marin and Mariano Torrisi
Symmetry 2021, 13(9), 1710; https://doi.org/10.3390/sym13091710
Received: 10 May 2021 / Revised: 11 July 2021 / Accepted: 1 September 2021 / Published: 16 September 2021
(This article belongs to the Special Issue Mathematical Aspects in Non-equilibrium Thermodynamics)
This paper is concerned with modeling nonequilibrium phenomena in spatial domains with boundaries. The resultant models consist of hyperbolic systems of first-order partial differential equations with boundary conditions (BCs). Taking a linearized moment closure system as an example, we show that the structural stability condition and the uniform Kreiss condition do not automatically guarantee the compatibility of the models with the corresponding classical models. This motivated the generalized Kreiss condition (GKC)—a strengthened version of the uniform Kreiss condition. Under the GKC and the structural stability condition, we show how to derive the reduced BCs for the equilibrium systems as the classical models. For linearized problems, the validity of the reduced BCs can be rigorously verified. Furthermore, we use a simple example to show how thus far developed theory can be used to construct proper BCs for equations modeling nonequilibrium phenomena in spatial domains with boundaries. View Full-Text
Keywords: hyperbolic relaxation system; structural stability condition; generalized Kreiss condition hyperbolic relaxation system; structural stability condition; generalized Kreiss condition
MDPI and ACS Style

Yong, W.-A.; Zhou, Y. Recent Advances on Boundary Conditions for Equations in Nonequilibrium Thermodynamics. Symmetry 2021, 13, 1710. https://doi.org/10.3390/sym13091710

AMA Style

Yong W-A, Zhou Y. Recent Advances on Boundary Conditions for Equations in Nonequilibrium Thermodynamics. Symmetry. 2021; 13(9):1710. https://doi.org/10.3390/sym13091710

Chicago/Turabian Style

Yong, Wen-An, and Yizhou Zhou. 2021. "Recent Advances on Boundary Conditions for Equations in Nonequilibrium Thermodynamics" Symmetry 13, no. 9: 1710. https://doi.org/10.3390/sym13091710

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