In this paper, we mainly study the stability of Riemann problem for the improved Aw–Rascle–Zhang model which describes the formation and dynamics of traffic jams. First of all, we construct the classical Riemann solutions by elementary waves with the method of characteristic analysis. With the generalized Rankine–Hugoniot and entropy conditions, we prove the existence and uniqueness of $\delta$-shock wave for arbitrary convex $F\left(u\right)$ in this model. Then through a small perturbation, we analyze the wave interactions of different kinds of waves. As a result, we get the stability for the Riemann problem by letting the perturbed parameter $\epsilon \to 0$.

中文翻译：

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具有Chaplygin压力的改进Aw-Rascle-Zhang模型的稳定性

在本文中，我们主要研究改进的Aw-Rascle-Zhang模型的Riemann问题的稳定性，该模型描述了交通拥堵的形成和动力学。首先，利用特征分析的方法，用基波构造了经典的黎曼解。利用广义兰金-Hugoniot和熵条件，我们证明了存在性和唯一性$\delta$任意凸的冲击波 $F（ü）$在这个模型中。然后通过一个小扰动，我们分析了不同种类的波的相互作用。结果，我们通过扰动参数来获得黎曼问题的稳定性$\epsilon \to 0$。