Approximate controllability for a stochastic elastic system with structural damping and infinite delay

被引：1

作者：

Peng, Jiankui ^{[2
]}

Gao, Xiang ^{[1
]}

Su, Yongbing ^{[3
]}

Kang, Xiaodong ^{[4
]}

机构：

[1] Lanzhou Univ Arts & Sci, Sch Digital Media, Lanzhou 730010, Peoples R China

[2] Lanzhou Univ Arts & Sci, Sch Educ, Lanzhou 730010, Peoples R China

[3] Lanzhou Jiaotong Univ, Sch Math & Phys, Lanzhou 730070, Peoples R China

[4] North China Elect Power Univ, Sch Control & Comp Engn, Beijing 102208, Peoples R China

来源：

OPEN MATHEMATICS | 2023年 / 21卷 / 01期

关键词：

approximate controllability; Stochastic elastic system; infinite delay; Wiener process; DIFFERENTIAL-EQUATIONS; EVOLUTION SYSTEM;

D O I：

10.1515/math-2023-0116

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we study the existence of mild solutions and the approximate controllability for a class of stochastic elastic systems with structural damping and infinite delay in Hilbert spaces. The estimation of the control function is discussed, where the expression of the control function is constructed by the defined resolvent operator. Under this estimate, the existence of mild solutions for this system is obtained by the Schauder fixed point theorem and the stochastic analysis theory, and sufficient conditions for the approximate controllability are formulated and proved by using the so-called resolvent operator type condition. Finally, an example is given to illustrate the applicability of our conclusion.

引用

页数：17

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