多预期车辆跟随交通模型的出行解决方案

IF 2.6 4区数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY

Mathematical Modelling of Natural Phenomena Pub Date : 2023-02-12 DOI:10.1051/mmnp/2023006

Nader El Khatib, Amine Ghorbel, Agatha Joumaa, Mamdouh Zaydan

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引用次数: 0

摘要

本文考虑了一个稳态多预期交通模型，给出了出行解存在的充要条件。在我们的工作中，“行驶”一词意味着两辆连续车辆之间的距离在两种不同的状态之间连续行驶。作为对结果的应用，我们证明了取一个严格凹的最优速度，我们可以构造一个行驶解，使两辆车之间的距离减小。这些解的存在性、唯一性和渐近性的研究是在Hamilton-Jacobi方程的水平上进行的。

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Traveling solutions for a multi-anticipative car-following traffic model

In this paper, we consider a steady state multi-anticipative traffic model and we provide necessarily and sufficient conditions for the existence of traveling solutions. In our work, the word "traveling" means that the distance between two consecutive vehicles travels continuously between two different states. As application to our result, we show that taking a strictly concave optimal velocity, we can construct a traveling solution such that the distance between two vehicles decreases. The existence, uniqueness and the study of the asymptotic behavior of such solutions is done at the level of the Hamilton-Jacobi equation.

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来源期刊

Mathematical Modelling of Natural Phenomena MATHEMATICAL & COMPUTATIONAL BIOLOGY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

5.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Mathematical Modelling of Natural Phenomena (MMNP) is an international research journal, which publishes top-level original and review papers, short communications and proceedings on mathematical modelling in biology, medicine, chemistry, physics, and other areas. The scope of the journal is devoted to mathematical modelling with sufficiently advanced model, and the works studying mainly the existence and stability of stationary points of ODE systems are not considered. The scope of the journal also includes applied mathematics and mathematical analysis in the context of its applications to the real world problems. The journal is essentially functioning on the basis of topical issues representing active areas of research. Each topical issue has its own editorial board. The authors are invited to submit papers to the announced issues or to suggest new issues. Journal publishes research articles and reviews within the whole field of mathematical modelling, and it will continue to provide information on the latest trends and developments in this ever-expanding subject.