{"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":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cms.2024.v22.n3.a9","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","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：
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.
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