一类具有瞬时脉冲的二阶发展方程的近似可控性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (2): 421-432.

一类具有瞬时脉冲的二阶发展方程的近似可控性

康笑东^*(),范虹霞()

兰州交通大学数理学院兰州 730070

收稿日期:2021-12-03 修回日期:2022-09-20 出版日期:2023-04-26 发布日期:2023-04-17
通讯作者: 康笑东，E-mail:kangxiaodong95@163.com
作者简介:范虹霞，E-mail:ffls0217@126.com
基金资助:
国家自然科学基金(11561040)

Approximate Controllability for a Class of Second-Order Evolution Equations with Instantaneous Impulse

Kang Xiaodong(),Fan Hongxia()

College of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070

Received:2021-12-03 Revised:2022-09-20 Online:2023-04-26 Published:2023-04-17
Supported by:
NSFC(11561040)

摘要/Abstract

摘要：

该文在 Hilbert 空间中研究一类具有无穷时滞和瞬时脉冲的二阶中立型发展方程的近似可控性. 利用余弦族理论得到该方程 mild 解的表示, 并结合 Schauder 不动点定理得到 mild 解的存在性结论. 通过构造一个适当的控制函数, 并利用预解算子型条件得到该方程近似可控的充分条件. 最后给出一个例子来说明主要结论的应用.

关键词: 近似可控性, 二阶中立型发展方程, 无穷时滞, 瞬时脉冲, 余弦族理论

Abstract:

In this paper, we study the approximate controllability for a class of second-order neutral evolution matrixs with infinite delay and instantaneous pulses in Hilbert spaces. The representation of mild solution of this matrix is obtained by using the cosine family theory, and combined with Schauder fixed point theorem, the existence conclusion of mild solution is obtained. By constructing an appropriate control function and using the resolvent operator type condition, the sufficient condition for the approximate controllability of this matrix is acquired. Finally, an example is given to illustrate the application of the main conclusions.

Key words: Approximate controllability, Second-order neutral evolution matrix, Infinite time delay, Instantaneous impulse, Cosine family theory

中图分类号:

O175.29

康笑东, 范虹霞. 一类具有瞬时脉冲的二阶发展方程的近似可控性[J]. 数学物理学报, 2023, 43(2): 421-432.

Kang Xiaodong, Fan Hongxia. Approximate Controllability for a Class of Second-Order Evolution Equations with Instantaneous Impulse[J]. Acta mathematica scientia,Series A, 2023, 43(2): 421-432.

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