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Interaction of elementary waves for the Aw–Rascle traffic flow model with variable lane width

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, Zhejiang Province, People’s Republic of China

    Qinglong Zhang

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Wancheng Sheng

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  1. Qinglong Zhang
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  2. Wancheng Sheng
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Correspondence to Wancheng Sheng.

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Zhang, Q., Sheng, W. Interaction of elementary waves for the Aw–Rascle traffic flow model with variable lane width. Z. Angew. Math. Phys. 72, 175 (2021). https://doi.org/10.1007/s00033-021-01606-7

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  • DOI: https://doi.org/10.1007/s00033-021-01606-7

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