连续统热力学的开放数学问题：双曲性，边界和非线性
Open mathematical aspects of continuum thermodynamics: hyperbolicity, boundaries and nonlinearities
摘要：
热力学在工程实践中不断发展，特别是在连续介质问题中的非平衡模型。虽然有超越经典知识的概念和方法，这是已知的几十年，他们的数学性质和推广的后果是鲜为人知的，仍然是当前研究的高度兴趣。因此，我们发现有必要收集最重要的和仍然开放的数学问题有关的不同的连续热力学方法。首先，我们从经典不可逆热力学（CIT）的例子开始，以便为更一般和更复杂的框架提供基础，例如具有内部变量的非平衡热力学（NET-IV）和理性扩展热力学（RET）。在这里，我们的目标是提出每种方法都有其特定的问题，如如何制定初始和边界条件，如何在偏微分方程中的系数是相互连接的，以及它如何影响非线性的外观。我们提出了这些属性，并从这些角度比较NET-IV和RET的方法。
英文摘要：
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 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.
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