自动驾驶汽车在交通中行驶：考奇问题

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Communications in Mathematical Sciences Pub Date : 2024-03-04 DOI:10.4310/cms.2024.v22.n3.a9

Mauro Garavello, Francesca Marcellini

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引用次数: 0

摘要

本文讨论了一个 PDE-ODE 模型的考奇问题，在该模型中，两个守恒定律系统，即[Rinaldo M. Colombo, Francesca Marcellini, and Michel Rascle, $\href{https://doi.org/10.1137/090752468}\{textrm{SIAM J. Appl.在合适的假设条件下，我们证明了全局时间内的存在性结果。

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Autonomous vehicles driving traffic: The Cauchy problem

This paper deals with the Cauchy problem for a PDE‑ODE model, where a system of two conservation laws, namely the Two-Phase macroscopic model proposed in [Rinaldo M. Colombo, Francesca Marcellini, and Michel Rascle, $\href{https://doi.org/10.1137/090752468}{\textrm{SIAM J. Appl. Math., 70(7):2652–2666, 2010}}$], is coupled with an ordinary differential equation describing the trajectory of an autonomous vehicle (AV), which aims to control the traffic flow. Under suitable assumptions, we prove a global-in-time existence result.

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来源期刊

Communications in Mathematical Sciences 数学-应用数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.