APPROXIMATE CONTROLLABILITY OF SECOND-ORDER SEMILINEAR EVOLUTION SYSTEMS WITH STATE-DEPENDENT INFINITE DELAY

被引：4

作者：

Su, Xiaofeng ^{[1
]}

Fu, Xianlong ^{[1
]}

机构：

[1] East China Normal Univ, Sch Math Sci, Shanghai Key Lab PMMP, Shanghai 200241, Peoples R China

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2020年 / 10卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Second-order evolution equation; approximate controllability; cosine operator; fundamental solution; fractional power operator; ABSTRACT DIFFERENTIAL-EQUATIONS; INTEGRODIFFERENTIAL INCLUSIONS; MODEL; WELLPOSEDNESS;

D O I：

10.11948/20190217

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the problem of approximate controllability for a class of semilinear second-order control systems with state-dependent delay. We establish some sufficient conditions for approximate controllability for this kind of systems by constructing fundamental solutions and using the resolvent condition and techniques on cosine family of linear operators. Particularly, theory of fractional power operators for cosine families is also applied to discuss the problem so that the obtained results can be applied to the systems involving derivatives of spatial variables. To illustrate the applications of the obtained results, two examples are presented in the end.

引用

页码：1118 / 1148

页数：31

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