In this paper, we consider the interaction of elementary waves for the Aw–Rascle (AR) traffic flow model with variable lane width. The model is established based on the conservation laws where the lane width is considered, and the variable spaces ahead of the vehicles can be viewed as a source term which is incorporated into the model. Stationary waves are involved as the ingredient of the elementary waves. We then discuss the interactions of stationary wave with rarefaction wave, shock wave and contact discontinuity respectively, and construct the solutions globally in the phase plane. The results may contribute to dealing with traffic jam problems in the future study.

在本文中，我们考虑了具有可变车道宽度的 Aw-Rascle (AR) 交通流模型的基本波的相互作用。该模型是根据考虑车道宽度的守恒定律建立的，可以将车辆前方的可变空间视为纳入模型的源项。驻波是作为基本波的组成部分。然后我们分别讨论驻波与稀疏波、激波和接触不连续性的相互作用，并在相平面上全局构建解。结果可能有助于在未来的研究中处理交通拥堵问题。