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.

中文翻译：

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非平衡热力学方程边界条件的新进展

本文关注的是在有边界的空间域中对非平衡现象进行建模。生成的模型由具有边界条件 (BC) 的一阶偏微分方程的双曲系统组成。以线性化力矩闭合系统为例，我们表明结构稳定性条件和均匀 Kreiss 条件并不能自动保证模型与相应经典模型的兼容性。这激发了广义克赖斯条件（GKC）——统一克赖斯条件的强化版本。在 GKC 和结构稳定性条件下，我们展示了如何将平衡系统的约化 BC 作为经典模型推导出来。对于线性化问题，可以严格验证简化的 BC 的有效性。此外，