Giuseppe Maria Coclite, Nicola De Nitti, Carlotta Donadello, Florian Peru
{"title":"Inverse Design and Boundary Controllability for the Chromatography System","authors":"Giuseppe Maria Coclite, Nicola De Nitti, Carlotta Donadello, Florian Peru","doi":"10.1007/s00032-024-00402-y","DOIUrl":null,"url":null,"abstract":"<p>We consider the prototypical example of the <span>\\(2\\times 2\\)</span> liquid chromatography system and characterize the set of initial data leading to a given attainable profile at <span>\\(t=T\\)</span>. For profiles that are not attainable at time <i>T</i>, we study a non-smooth optimization problem: recovering the initial data that lead as close as possible to the target in the <span>\\(L^2\\)</span>-norm. We then study the system on a bounded domain and use a boundary control to steer its dynamics to a given trajectory. Finally, we implement a suitable finite volumes scheme to illustrate these results and show its numerical convergence. Minor modifications of our arguments apply to the Keyfitz–Kranzer system.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"22 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Milan Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00032-024-00402-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the prototypical example of the \(2\times 2\) liquid chromatography system and characterize the set of initial data leading to a given attainable profile at \(t=T\). For profiles that are not attainable at time T, we study a non-smooth optimization problem: recovering the initial data that lead as close as possible to the target in the \(L^2\)-norm. We then study the system on a bounded domain and use a boundary control to steer its dynamics to a given trajectory. Finally, we implement a suitable finite volumes scheme to illustrate these results and show its numerical convergence. Minor modifications of our arguments apply to the Keyfitz–Kranzer system.
期刊介绍：
Milan Journal of Mathematics (MJM) publishes high quality articles from all areas of Mathematics and the Mathematical Sciences. The authors are invited to submit "articles with background", presenting a problem of current research with its history and its developments, the current state and possible future directions. The presentation should render the article of interest to a wider audience than just specialists.
Many of the articles will be "invited contributions" from speakers in the "Seminario Matematico e Fisico di Milano". However, also other authors are welcome to submit articles which are in line with the "Aims and Scope" of the journal.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
