{"title":"Global boundary stabilization to trajectories of the deterministic and stochastic porous-media equation","authors":"Ionuţ Munteanu","doi":"10.3934/mcrf.2023037","DOIUrl":null,"url":null,"abstract":"Here we deal with the problem of boundary asymptotic exponential stabilization of flows through porous media. More exactly we study the porous media equation with general monotone porosity in a bounded domain of dimension $ d = 1,2,3 $. We construct an explicit, linear, of finite-dimensional structure feedback controller with Dirichlet part-boundary actuation, which stabilizes any trajectory of the system, for any given initial data. The form of the controller is based on the spectrum of the Dirichlet-Laplace operator and ensures exponential decay to zero of the fluctuation variable for any a priori prescribed decay rate. Also, we extend these results to the case of porous media equation perturbed by Itô Lipschitz noise.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/mcrf.2023037","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
Here we deal with the problem of boundary asymptotic exponential stabilization of flows through porous media. More exactly we study the porous media equation with general monotone porosity in a bounded domain of dimension $ d = 1,2,3 $. We construct an explicit, linear, of finite-dimensional structure feedback controller with Dirichlet part-boundary actuation, which stabilizes any trajectory of the system, for any given initial data. The form of the controller is based on the spectrum of the Dirichlet-Laplace operator and ensures exponential decay to zero of the fluctuation variable for any a priori prescribed decay rate. Also, we extend these results to the case of porous media equation perturbed by Itô Lipschitz noise.
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.