一类具有瞬时脉冲的二阶发展方程的近似可控性  

Approxima te Cont rollability for a Class of Second-Order Evolution Equations with Instantaneous Impulse

作　　者：康笑东 范虹霞[1] Kang Xiaodong;Fan Hongxia(College of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《数学物理学报（A辑）》2023年第2期421-432,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11561040)。

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.In this paper,we study the approximate controllability for a class of second-order neutral evolution equations with infinite delay and instantaneous pulses in Hilbert spaces.The representation of mild solution of this equation 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 equation is acquired.Finally,an example is given to illustrate the application of the main conclusions.

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 

分 类 号：O175.29[理学—数学]