论文标题
连续热力学的开放数学方面：双曲线，边界和非线性
Open mathematical aspects of continuum thermodynamics: hyperbolicity, boundaries and nonlinearities
论文作者
论文摘要
热力学在工程实践中不断扩散，这对于连续性问题中的非平衡模型尤其如此。尽管除经典知识以外的概念和方法已知数十年，但它们的数学特性和概括的后果鲜为人知，并且对当前的研究仍然具有很高的兴趣。因此，我们发现收集与不同的连续体热力学方法相关的最重要且仍然开放的数学问题至关重要。首先，我们从经典不可逆热力学（CIT）的示例开始，以为更通用和复杂的框架（例如具有内部变量（Net-IV）的非平衡热力学和合理的扩展热力学（RET）提供基础。在这里，我们的目的是介绍每种方法都有其特定问题，例如如何制定初始条件和边界条件，偏微分方程中的系数如何相互连接，以及如何影响非线性的外观。我们介绍了这些属性，并从这些角度将Net-IV和RET的方法相互比较。
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.
