In this paper, we analyze the behavior of viscous shock profiles of one-dimensional compressible Navier-Stokes equations with a singular pressure law which encodes the effects of congestion. As the intensity of the singular pressure tends to 0, we show the convergence of these profiles towards free-congested traveling front solutions of a two-phase compressible-incompressible Navier-Stokes system and we provide a refined description of the profiles in the vicinity of the transition between the free domain and the congested domain. In the second part of the paper, we prove that the profiles are asymptotically nonlinearly stable under small perturbations with zero integral, and we quantify the size of the admissible perturbations in terms of the intensity of the singular pressure.

中文翻译：

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一维 Navier-Stokes 模型中部分拥挤传播前沿的存在性和稳定性

在本文中，我们分析了一维可压缩 Navier-Stokes 方程的粘性冲击曲线的行为，该方程具有编码拥塞效应的奇异压力定律。由于奇异压力的强度趋于 0，我们展示了这些轮廓向两相可压缩 - 不可压缩纳维 - 斯托克斯系统的自由拥挤行进前沿解的收敛，我们提供了附近轮廓的精细描述自由域和拥塞域之间的过渡。在论文的第二部分，我们证明了轮廓在零积分的小扰动下是渐近非线性稳定的，并且我们根据奇异压力的强度量化了容许扰动的大小。