{"title":"论半线性演化方程的精确全局可控性","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":50580,"journal":{"name":"Differential Equations","volume":"144 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":50580,\"journal\":{\"name\":\"Differential Equations\",\"volume\":\"144 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-07-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0012266124030091\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124030091","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Exact Global Controllability of a Semilinear Evolution Equation
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.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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