时空非局部交通流模型:松弛表示和局部极限

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-11-02 DOI:10.3934/dcds.2023054

Q. Du, Kuang Huang, J. Scott, Wen Shen

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引用次数: 1

摘要

提出并研究了一种非局部守恒律，用于模拟存在车辆间通信的交通流。假设非局部信息以有限速度传播，模型涉及加权交通密度的时空非局部积分。在适当的模型参数条件和适当的初始条件下，建立了模型的适定性。在非局部积分的权核为指数函数的特殊情况下，非局部模型可以重新表述为一个2\times2$带松弛的双曲系统。借助这种松弛表示，我们证明了Lighthill-Whitham-Richards模型是在平衡近似极限下恢复的。

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A space-time nonlocal traffic flow model: Relaxation representation and local limit

We propose and study a nonlocal conservation law modelling traffic flow in the existence of inter-vehicle communication. It is assumed that the nonlocal information travels at a finite speed and the model involves a space-time nonlocal integral of weighted traffic density. The well-posedness of the model is established under suitable conditions on the model parameters and by a suitably-defined initial condition. In a special case where the weight kernel in the nonlocal integral is an exponential function, the nonlocal model can be reformulated as a $2\times2$ hyperbolic system with relaxation. With the help of this relaxation representation, we show that the Lighthill-Whitham-Richards model is recovered in the equilibrium approximation limit.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.