具有结构阻尼的弹性系统的近似可控性
Approximate Controllability of Elastic Systems with Structural Damping
- 武汉大学学报（理学版）
- 作者机构：
1.兰州交通大学 数理学院，甘肃 兰州 730070
2.甘肃财贸职业学院 信息技术系，甘肃 兰州730207
- 作者简介：
康笑东，男，硕士生，现从事非线性发展方程方面的研究。E-mail：kangxiaodong95@163.com
- 基金信息：国家自然科学基金(11561040;11961039);甘肃省自然科学基金(20JR5RA418)
DOI：10.14188/j.1671-8836.2021.0011
中图分类号： O175.23纸质出版日期：2021-04-24，
收稿日期：2021-01-16，
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康笑东,邵勇,范虹霞.具有结构阻尼的弹性系统的近似可控性[J].武汉大学学报（理学版）,2021,67(2):151-157.
KANG Xiaodong,SHAO Yong,FAN Hongxia.Approximate Controllability of Elastic Systems with Structural Damping [J].J Wuhan Univ （Nat Sci Ed）,2021,67(2):151-157.
康笑东,邵勇,范虹霞.具有结构阻尼的弹性系统的近似可控性[J].武汉大学学报（理学版）,2021,67(2):151-157. DOI：10.14188/j.1671-8836.2021.0011
KANG Xiaodong,SHAO Yong,FAN Hongxia.Approximate Controllability of Elastic Systems with Structural Damping [J].J Wuhan Univ （Nat Sci Ed）,2021,67(2):151-157. DOI：10.14188/j.1671-8836.2021.0011(Ch).
摘要
在Banach空间中研究具有结构阻尼的弹性系统的近似可控性。利用Banach压缩映像原理、Schauder不动点定理， 研究了具有控制项的阻尼弹性控制系统mild解的存在唯一性；同时，利用算子半群理论并结合值域型条件， 通过构造收敛的序列， 获得了具有结构阻尼的弹性系统的近似可控性，丰富和发展了阻尼弹性系统已有的结果。
Abstract
In this paper, we study the approximate controllability of elastic systems with structural damping in Banach spaces. By using the principle of the Banach contractive mapping and the Schauder fixed point theorem, we study the existence and uniqueness of mild solutions of damped elastic control systems with control terms. At the same time, by using the theory of operator semigroup and combining the conditions of value domain types, we construct a convergent sequence, and obtain the approximate controllability of elastic systems with structural damping, which enriches and develops the existing results of damped elastic systems.
关键词
结构阻尼近似可控性不动点mild解
Keywords
structural dampingapproximate controllabilityfixed pointmild solution
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