{"title":"关于BBM方程的可控性","authors":"Melek Jellouli","doi":"10.3934/mcrf.2022002","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>In this article, we consider the nonlinear BBM equation on the torus. We use controls taking values in a finite dimensional space to show that the equation is approximately controllable in <inline-formula><tex-math id=\"M1\">\\begin{document}$ H^1(\\mathbb{T}) $\\end{document}</tex-math></inline-formula>. We also show that the equation is not exactly controllable in <inline-formula><tex-math id=\"M2\">\\begin{document}$ H^s(\\mathbb{T}) $\\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id=\"M3\">\\begin{document}$ s\\in[1,2[ $\\end{document}</tex-math></inline-formula>.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the controllability of the BBM equation\",\"authors\":\"Melek Jellouli\",\"doi\":\"10.3934/mcrf.2022002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p style='text-indent:20px;'>In this article, we consider the nonlinear BBM equation on the torus. We use controls taking values in a finite dimensional space to show that the equation is approximately controllable in <inline-formula><tex-math id=\\\"M1\\\">\\\\begin{document}$ H^1(\\\\mathbb{T}) $\\\\end{document}</tex-math></inline-formula>. We also show that the equation is not exactly controllable in <inline-formula><tex-math id=\\\"M2\\\">\\\\begin{document}$ H^s(\\\\mathbb{T}) $\\\\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id=\\\"M3\\\">\\\\begin{document}$ s\\\\in[1,2[ $\\\\end{document}</tex-math></inline-formula>.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/mcrf.2022002\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/mcrf.2022002","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
In this article, we consider the nonlinear BBM equation on the torus. We use controls taking values in a finite dimensional space to show that the equation is approximately controllable in \begin{document}$ H^1(\mathbb{T}) $\end{document}. We also show that the equation is not exactly controllable in \begin{document}$ H^s(\mathbb{T}) $\end{document} for \begin{document}$ s\in[1,2[ $\end{document}.
In this article, we consider the nonlinear BBM equation on the torus. We use controls taking values in a finite dimensional space to show that the equation is approximately controllable in \begin{document}$ H^1(\mathbb{T}) $\end{document}. We also show that the equation is not exactly controllable in \begin{document}$ H^s(\mathbb{T}) $\end{document} for \begin{document}$ s\in[1,2[ $\end{document}.
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.
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
