We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems.

中文翻译：

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一维混合双曲抛物线系统的特征边界层及其在 Navier-Stokes 和 MHD 方程中的应用

我们提供了一个空间维度和小振幅范围内混合双曲抛物线系统的边界层的详细分析。作为我们结果的应用，我们描述了所谓的边界黎曼问题的解决方案，该问题恢复为物理粘性近似的零粘度极限。特别是，我们解决了所谓的双特征情况，从技术角度来看，这种情况要求更高，并且当边界对混合双曲抛物线系统和通过忽略二阶项获得的双曲系统都具有特征时会发生。我们的分析特别适用于欧拉坐标中的可压缩 Navier-Stokes 和 MHD 方程，具有正电导率和零电导率。在这些情况下，