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Open Mathematical Aspects of Continuum Thermodynamics: Hyperbolicity, Boundaries and Nonlinearities

1
Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary
2
Montavid Thermodynamic Research Group, 1112 Budapest, Hungary
3
Department of Theoretical Physics, Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, 1525 Budapest, Hungary
4
Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, 21000 Novi Sad, Serbia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(9), 1469; https://doi.org/10.3390/sym12091469
Received: 30 July 2020 / Revised: 1 September 2020 / Accepted: 2 September 2020 / Published: 7 September 2020
Thermodynamics is continuously spreading in the engineering practice, which is especially true for non-equilibrium models in continuum problems. Although there are concepts and approaches beyond the classical knowledge, which are known for decades, their mathematical properties, and consequences of the generalizations are less-known and are still of high interest in current researches. Therefore, we found it essential to collect the most important and still open mathematical questions that are related to different continuum thermodynamic approaches. First, we start with the example of Classical Irreversible Thermodynamics (CIT) in order to provide the basis for the more general and complex frameworks, such as the Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and Rational Extended Thermodynamics (RET). Here, we aim to present that each approach has its specific problems, such as how the initial and boundary conditions can be formulated, how the coefficients in the partial differential equations are connected to each other, and how it affects the appearance of nonlinearities. We present these properties and comparing the approach of NET-IV and RET to each other from these points of view. In the present work, we restrict ourselves on non-relativistic models. View Full-Text
Keywords: rational extended thermodynamics; non-equilibrium thermodynamics with internal variables; initial and boundary conditions; close problems; nonlinearities rational extended thermodynamics; non-equilibrium thermodynamics with internal variables; initial and boundary conditions; close problems; nonlinearities
MDPI and ACS Style

Szücs, M.; Kovács, R.; Simić, S. Open Mathematical Aspects of Continuum Thermodynamics: Hyperbolicity, Boundaries and Nonlinearities. Symmetry 2020, 12, 1469.

AMA Style

Szücs M, Kovács R, Simić S. Open Mathematical Aspects of Continuum Thermodynamics: Hyperbolicity, Boundaries and Nonlinearities. Symmetry. 2020; 12(9):1469.

Chicago/Turabian Style

Szücs, Mátyás; Kovács, Róbert; Simić, Srboljub. 2020. "Open Mathematical Aspects of Continuum Thermodynamics: Hyperbolicity, Boundaries and Nonlinearities" Symmetry 12, no. 9: 1469.

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