{"title":"Autonomous vehicles driving traffic: The Cauchy problem","authors":"Mauro Garavello, Francesca Marcellini","doi":"10.4310/cms.2024.v22.n3.a9","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"42 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cms.2024.v22.n3.a9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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。
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.