Roberto de A. Capistrano-Filho, Luan S. de Sousa, Fernando A. Gallego
{"title":"Approximation theorem for the Kawahara operator and its application in the control theory","authors":"Roberto de A. Capistrano-Filho, Luan S. de Sousa, Fernando A. Gallego","doi":"10.1002/mana.202300235","DOIUrl":null,"url":null,"abstract":"<p>Control properties of the Kawahara equation are considered when the equation is posed on an unbounded domain. Precisely, the paper's main results are related to an approximation theorem that ensures the exact (internal) controllability in <span></span><math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mn>0</mn>\n <mo>,</mo>\n <mo>+</mo>\n <mi>∞</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$(0,+\\infty)$</annotation>\n </semantics></math>. Following [23], the problem is reduced to prove an approximate theorem which is achieved thanks to a global Carleman estimate for the Kawahara operator.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300235","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Control properties of the Kawahara equation are considered when the equation is posed on an unbounded domain. Precisely, the paper's main results are related to an approximation theorem that ensures the exact (internal) controllability in . Following [23], the problem is reduced to prove an approximate theorem which is achieved thanks to a global Carleman estimate for the Kawahara operator.