The pressureless transition of Riemann solutions containing composite waves for Aw–Rascle–Zhang model with driver adaptation

Weifeng Jiang; Chengxin Gao; Tingting Chen; Tong Li; Zhen Wang

doi:10.1016/j.chaos.2026.118258

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The pressureless transition of Riemann solutions containing composite waves for Aw–Rascle–Zhang model with driver adaptation

Journal article

Peer reviewed

The pressureless transition of Riemann solutions containing composite waves for Aw–Rascle–Zhang model with driver adaptation

Weifeng Jiang, Chengxin Gao, Tingting Chen, Tong Li and Zhen Wang

Chaos, solitons and fractals, Vol.208, 118258

07/2026

DOI: 10.1016/j.chaos.2026.118258

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Abstract

In this paper, we focus on the pressureless limiting behaviors of the Riemann solutions for Aw-Rascle–Zhang (ARZ) model with density-adaptive drivers. We construct the Riemann solutions containing composite waves by the ‘‘Liu-entropy’’ condition due to the non-genuine nonlinearity of this traffic flow system. Then we investigate the limiting dynamics of the Riemann solutions and demonstrate the formation of 𝛿−shock waves and vacuum states as the pressure vanishes. Finally, numerical simulations are performed to validate the theoretical results. Two highlights are noteworthy. First, composite waves persist during the pressure vanishing process under certain conditions. Second, we find a new mechanism in cavitation formation that as the pressure vanishes, the Riemann solution containing shock waves converges to the vacuum solution of the pressureless gas dynamics model in specific configurations.

Riemann problem

Vanishing pressure limit

Composite wave

delta-shock wave

Vacuum

Aw-Rascle-Zhang model

Details

Title: Subtitle: The pressureless transition of Riemann solutions containing composite waves for Aw–Rascle–Zhang model with driver adaptation
Creators: Weifeng Jiang - China Jiliang University
Chengxin Gao - China Jiliang University
Tingting Chen - Jianghan University
Tong Li - University of Iowa
Zhen Wang - Wuhan University of Technology
Resource Type: Journal article
Publication Details: Chaos, solitons and fractals, Vol.208, 118258
DOI: 10.1016/j.chaos.2026.118258
ISSN: 0960-0779
eISSN: 1873-2887
Publisher: Elsevier
Grant note: Natural Science Foundation of China: 1240012056 Research Fund of Jianghan University: 2024JCYJ05
The authors would like to thank the editors and referees for providing very useful suggestions to improve the presentation in paper. The research of Weifeng Jiang is supported by Natural Science Foundation of China (Grant No. 1240012056) . The research of Tingting Chen is supported by the Research Fund of Jianghan University (Grant No. 2024JCYJ05) .
Language: English
Date published: 07/2026
Academic Unit: Mathematics
Record Identifier: 9985149523902771

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