Stability and regularity transmission for coupled beam and wave equations through boundary weak connections

doi:10.1051/cocv/2019056

	Stability and regularity transmission for coupled beam and wave equations through boundary weak connections
	Guo, Bao-Zhu 1,2,3; Ren, Han-Jing 1,3
刊名	ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
	2020-09-30
卷号	26 页码:29
关键词	Euler-Bernoulli beam equation wave equation with structural damping coupled system Gevrey class
ISSN号	1292-8119
DOI	10.1051/cocv/2019056
英文摘要	In this paper, we consider stability for a hyperbolic-hyperbolic coupled system consisting of Euler-Bernoulli beam and wave equations, where the structural damping of the wave equation is taken into account. The coupling is actuated through boundary weak connection in the sense that after differentiation of the total energy for coupled system, only the term of the wave equation appears explicitly. We first show that the spectrum of the closed-loop system consists of three branches: one branch is basically along the real axis and accumulates to a finite point; the second branch is also along the real line; and the third branch distributes along two parabola likewise symmetric with the real axis. The asymptotic expressions of both eigenvalues and eigenfunctions are obtained by means of asymptotic analysis. With an estimation of the resolvent operator, the completeness of the root subspace is proved. The Riesz basis property and exponential stability of the system are then concluded. Finally, we show that the associated C-0-semigroup is of Gevrey class, which shows that not only the stability but also regularity have been transmitted from regular wave subsystem to the whole system through this boundary connections.
资助项目	National Natural Science Foundation of China[61873260] ; Project of Department of Education of Guangdong Province[2017KZDXM087]
WOS研究方向	Automation & Control Systems ; Mathematics
语种	英语
出版者	EDP SCIENCES S A
WOS记录号	WOS:000577110600004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52287]
专题	中国科学院数学与系统科学研究院
通讯作者	Guo, Bao-Zhu
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 2.North China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Guo, Bao-Zhu,Ren, Han-Jing. Stability and regularity transmission for coupled beam and wave equations through boundary weak connections[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS,2020,26:29.
APA	Guo, Bao-Zhu,&Ren, Han-Jing.(2020).Stability and regularity transmission for coupled beam and wave equations through boundary weak connections.ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS,26,29.
MLA	Guo, Bao-Zhu,et al."Stability and regularity transmission for coupled beam and wave equations through boundary weak connections".ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 26(2020):29.