Two kinds of Riemann solutions for the Aw-Rascle hydrodynamic traffic flow model with the logarithmic equation of state are explicitly obtained by using the combination between 1-rarefaction or 1-shock wave along with 2-contact discontinuity. The formation of vacuum state and delta shock wave is identified and analyzed when the perturbation parameter in the pressure term drops to zero, where the intrinsic cavitation and concentration phenomena are surveyed and explored concretely. Additionally, several numerical results displaying the formation process of vacuum state and delta shock wave are also presented by taking three different perturbation parameters for comparison.

中文翻译：

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对数状态方程Aw-Rascle水动力交通流模型黎曼解的消失压力极限

利用1-稀疏或1-冲击波与2-接触不连续性的组合，明确获得了具有对数状态方程的Aw-Rascle水动力交通流模型的两种黎曼解。识别并分析了压力项中的摄动参数降为零时真空态和δ激波的形成，具体考察和探讨了固有的空化和浓缩现象。此外，还通过比较三种不同的摄动参数，给出了显示真空态和δ激波形成过程的几个数值结果。