{"title":"An optimal control problem for diffusion–precipitation model1","authors":"A. Kundu, H. S. Mahato","doi":"10.3233/asy-241905","DOIUrl":null,"url":null,"abstract":"We present an optimal control problem associated to a chemical transportation phenomena in a periodic porous medium. Posing controls on the porous part of the medium (distributed control), we set up a convex minimization problem. The main objective of this article is to characterize an arbitrary control to be an optimal control. We establish a relation between the optimal control and the corresponding adjoint state. At first, we analyse the microscopic description of the controlled system, then we homogenised the system by rigorous two-scale convergence method and periodic unfolding method.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-04-23","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/10.3233/asy-241905","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
We present an optimal control problem associated to a chemical transportation phenomena in a periodic porous medium. Posing controls on the porous part of the medium (distributed control), we set up a convex minimization problem. The main objective of this article is to characterize an arbitrary control to be an optimal control. We establish a relation between the optimal control and the corresponding adjoint state. At first, we analyse the microscopic description of the controlled system, then we homogenised the system by rigorous two-scale convergence method and periodic unfolding method.
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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