一类改进的 Aw-Rascle-Zhang 模型的柯西问题

数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 1025-1027.

一类改进的 Aw-Rascle-Zhang 模型的柯西问题

陈停停¹(), 蒋伟峰²^,^*(), 李彤³(), 来意博²()

¹ 江汉大学人工智能学院武汉 430056
² 中国计量大学理学院杭州 310018
³ 爱荷华大学数学学院爱荷华 IA 52242

收稿日期:2024-11-11 修回日期:2025-10-21 出版日期:2026-06-26 发布日期:2026-06-16
通讯作者: 蒋伟峰 E-mail:chenting0617@163.com;casujiang89@cjlu.edu.cn;tong-li@uiowa.edu;2200805210@cjlu.edu.cn
作者简介:陈停停, E-mail:chenting0617@163.com;
李彤, E-mail:tong-li@uiowa.edu;
来意博, E-mail:2200805210@cjlu.edu.cn
基金资助:
国家自然科学基金(1240012056);江汉大学科研基金(2024JCYJ05)

The Cauchy Problem for an Improved Aw-Rascle-Zhang Model

Tingting Chen¹(), Weifeng Jiang²^,^*(), Tong Li³(), Yibo Lai²()

¹ School of Artificial Intelligence, Jianghan University, Wuhan 430056
² 2College of Science, China Jiliang University, Hangzhou 310018
³ Department of Mathematics, The University of Iowa, Iowa City, IA 52242

Received:2024-11-11 Revised:2025-10-21 Online:2026-06-26 Published:2026-06-16
Contact: Weifeng Jiang E-mail:chenting0617@163.com;casujiang89@cjlu.edu.cn;tong-li@uiowa.edu;2200805210@cjlu.edu.cn
Supported by:
NSFC(1240012056);Research Fund of Jianghan University(2024JCYJ05)

摘要/Abstract

摘要：

该文研究具有非真正非线性场的改进的 Aw-Rascle-Zhang 交通流模型的柯西问题. 该模型的黎曼解结构中不仅包含激波, 稀疏波和接触间断, 还包含复合波. 该文在有界变差函数空间框架下, 发展了一种基于修正的 Glimm 差分格式的方法. 该方法的关键在于利用黎曼不变量的变差构造了波相互作用泛函, 并以此控制解在时间演化过程中的总变差. 从而证明了大初值情形下柯西问题全局弱解的存在性.

关键词: 柯西问题, 改进的 Aw-Rascle-Zhang 模型, 修正的 Glimm 格式, BV 解, 大初值.

Abstract:

This paper studies the Cauchy problem for an improved Aw-Rascle-Zhang traffic flow model exhibiting non-genuine nonlinearity. The Riemann solution structure for this model contains not only shocks, rarefaction waves, and contact discontinuities, but also composite waves. A method based on a modified Glimm scheme is developed within the framework of the space of functions of bounded variation. The key aspect of this method lies in constructing a wave interaction functional using the variation of Riemann invariants, thereby controlling the total variation of the solution during its time evolution. Therefore we establish the existence of a global weak solution for the Cauchy problem with large initial data.

Key words: cauchy problem, improved Aw-Rascle-Zhang model, modified Glimm's scheme, BV solutions, large initial data.

中图分类号:

O175.23

陈停停, 蒋伟峰, 李彤, 来意博. 一类改进的 Aw-Rascle-Zhang 模型的柯西问题[J]. 数学物理学报, 2026, 46(3): 1025-1027.

Tingting Chen, Weifeng Jiang, Tong Li, Yibo Lai. The Cauchy Problem for an Improved Aw-Rascle-Zhang Model[J]. Acta mathematica scientia,Series A, 2026, 46(3): 1025-1027.

图/表 5

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