{"title":"Banach空间中有限时滞偏泛函积分微分方程的近似边界可控性","authors":"P. Ndambomve, Shuqin Che","doi":"10.3934/eect.2022050","DOIUrl":null,"url":null,"abstract":"This work concerns the study of approximate boundary controllability for some nonlinear partial functional integrodifferential equations with finite delay arising in the modeling of materials with memory, in the framework of general Banach spaces. We give sufficient conditions that ensure the approximate controllability of the system by supposing that its linear undelayed part is approximately controllable, admits a resolvent operator in the sense of Grimmer, and by making use of the Banach fixed-point Theorem and the continuity of the resolvent operator in the uniform norm-topology. As a result, we obtain a generalization of several important results in the literature, without assuming the compactness of the resolvent operator and the uniform boundedness of the nonlinear term. An example of applications is given for illustration.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"12 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the approximate boundary controllability of some partial functional integrodifferential equations with finite delay in Banach spaces\",\"authors\":\"P. Ndambomve, Shuqin Che\",\"doi\":\"10.3934/eect.2022050\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work concerns the study of approximate boundary controllability for some nonlinear partial functional integrodifferential equations with finite delay arising in the modeling of materials with memory, in the framework of general Banach spaces. We give sufficient conditions that ensure the approximate controllability of the system by supposing that its linear undelayed part is approximately controllable, admits a resolvent operator in the sense of Grimmer, and by making use of the Banach fixed-point Theorem and the continuity of the resolvent operator in the uniform norm-topology. As a result, we obtain a generalization of several important results in the literature, without assuming the compactness of the resolvent operator and the uniform boundedness of the nonlinear term. An example of applications is given for illustration.\",\"PeriodicalId\":48833,\"journal\":{\"name\":\"Evolution Equations and Control Theory\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Evolution Equations and Control Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/eect.2022050\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Evolution Equations and Control Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/eect.2022050","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the approximate boundary controllability of some partial functional integrodifferential equations with finite delay in Banach spaces
This work concerns the study of approximate boundary controllability for some nonlinear partial functional integrodifferential equations with finite delay arising in the modeling of materials with memory, in the framework of general Banach spaces. We give sufficient conditions that ensure the approximate controllability of the system by supposing that its linear undelayed part is approximately controllable, admits a resolvent operator in the sense of Grimmer, and by making use of the Banach fixed-point Theorem and the continuity of the resolvent operator in the uniform norm-topology. As a result, we obtain a generalization of several important results in the literature, without assuming the compactness of the resolvent operator and the uniform boundedness of the nonlinear term. An example of applications is given for illustration.
期刊介绍:
EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include:
* Modeling of physical systems as infinite-dimensional processes
* Direct problems such as existence, regularity and well-posedness
* Stability, long-time behavior and associated dynamical attractors
* Indirect problems such as exact controllability, reachability theory and inverse problems
* Optimization - including shape optimization - optimal control, game theory and calculus of variations
* Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s)
* Applications of the theory to physics, chemistry, engineering, economics, medicine and biology