{"title":"On the Exact Global Controllability of a Semilinear Evolution Equation","authors":"A. V. Chernov","doi":"10.1134/s0012266124030091","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> For the Cauchy problem associated with a controlled semilinear evolution equation with\nan operator (not necessarily bounded) in a Hilbert space, we obtain sufficient conditions for exact\ncontrollability into a given terminal state (and also into given intermediate states at interim time\nmoments) on an arbitrarily fixed (without additional constraints) time interval. Here we use the\nBrowder—Minty theorem and also a chain technology of successive continuation of the solution of\nthe controlled system to intermediate states. As examples, we consider a semilinear\npseudoparabolic equation and a semilinear wave equation.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124030091","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
For the Cauchy problem associated with a controlled semilinear evolution equation with
an operator (not necessarily bounded) in a Hilbert space, we obtain sufficient conditions for exact
controllability into a given terminal state (and also into given intermediate states at interim time
moments) on an arbitrarily fixed (without additional constraints) time interval. Here we use the
Browder—Minty theorem and also a chain technology of successive continuation of the solution of
the controlled system to intermediate states. As examples, we consider a semilinear
pseudoparabolic equation and a semilinear wave equation.
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