This paper is devoted to studying the inflow problem for an ideal polytropic model with non-viscous gas in one-dimensional half space. We show the existence of the boundary layer in different areas. By employing the energy method, we also prove the unique global-in-time existence of the solution and the asymptotic stability of both the boundary layers, the $3$‑rarefaction wave and their superposition wave under some smallness conditions. Series of simple but tricky operations on boundary need to be carefully done by taking good advantage of construction on the system and domain properties.

中文翻译：

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边界问题的稀疏波和稀疏波的非线性稳定性，用于由无粘性的导热理想气体控制的流入问题

本文致力于研究一维半空间中具有非粘性气体的理想多方模型的流入问题。我们显示了边界层在不同区域中的存在。通过采用能量方法，我们还证明了解的唯一全局时间存在性以及在某些较小条件下边界层，$ 3 $-反射波和它们的叠加波这两个边界层的渐近稳定性。需要充分利用系统和域属性的构造优势，仔细进行一系列简单但棘手的边界操作。