Starting with this paper, we intend to develop a program aiming at construction of boundary conditions (BCs) for hyperbolic relaxation systems. Physically, such BCs are not always available. The construction is based on the assumption that the relaxation systems and well-posed BCs for the corresponding equilibrium systems are given. This paper focuses on the linearized Suliciu model. We obtain strictly dissipative and compatible BCs for the linearized model with different non-characteristic boundaries. Moreover, the effectiveness of the constructed BCs is shown by resorting to formal asymptotic solutions and energy estimates.

中文翻译：

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双曲松弛近似边界条件的构建 I：线性化的 Suliciu 模型

从本文开始，我们打算开发一个旨在为双曲线松弛系统构建边界条件（BC）的程序。在物理上，这样的 BC 并不总是可用的。该构造基于以下假设：已给出相应平衡系统的松弛系统和适定 BC。本文重点研究线性化的苏利丘模型。我们为具有不同非特征边界的线性化模型获得了严格耗散和兼容的 BC。此外，通过采用正式的渐近解和能量估计来证明构建的 BCs 的有效性。