Exponential Stabilization of the Wave Equation on Hyperbolic Spaces with Nonlinear Locally Distributed Damping

doi:10.1007/s00245-021-09751-1

CSpace

	Exponential Stabilization of the Wave Equation on Hyperbolic Spaces with Nonlinear Locally Distributed Damping
	Wang, Jiacheng 1,2; Ning, Zhen-Hu 3; Yang, Fengyan 4
	2021-01-30
发表期刊	APPLIED MATHEMATICS AND OPTIMIZATION
ISSN	0095-4616
页码	13
摘要	In this article, we consider the wave equation on hyperbolic spaces H-n(n >= 2) with nonlinear locally distributed damping as follow: {u(tt) - Delta(g)u + a(x)g(u(t)) = 0 (x, t) is an element of H-n x (0,+infinity),(1) u(x, 0) = u(0)(x), u(0)(x, 0) = u(1)(x) x is an element of H-n. It is well-known that the energy of the system (1) is of polynomial decay in the Euclidean space. However, on hyperbolic spaces, owing to the following inequality integral(Hn) u(2)dx(g) <= C integral(Hn) \|del(g)u\|(2)(g)dx(g), f or u is an element of H-1 (H-n), (2) we prove the exponential stabilization of the wave equation by multiplier methods and compactness-uniqueness arguments.
关键词	Wave equation Stabilization Hyperbolic spaces Nonlinear locally distributed damping
DOI	10.1007/s00245-021-09751-1
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[61573342] ; Key Research Program of Frontier Sciences, Chinese Academy of Sciences[QYZDJ-SSW-SYS011] ; Fundamental Research Funds for the Central Universities
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000613037600001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58092
专题	中国科学院数学与系统科学研究院
通讯作者	Yang, Fengyan
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 3.Beijing Univ Technol, Fac Informat Technol, Beijing 100124, Peoples R China 4.Beijing Forestry Univ, Sch Sci, Beijing 100083, Peoples R China
推荐引用方式 GB/T 7714	Wang, Jiacheng,Ning, Zhen-Hu,Yang, Fengyan. Exponential Stabilization of the Wave Equation on Hyperbolic Spaces with Nonlinear Locally Distributed Damping[J]. APPLIED MATHEMATICS AND OPTIMIZATION,2021:13.
APA	Wang, Jiacheng,Ning, Zhen-Hu,&Yang, Fengyan.(2021).Exponential Stabilization of the Wave Equation on Hyperbolic Spaces with Nonlinear Locally Distributed Damping.APPLIED MATHEMATICS AND OPTIMIZATION,13.
MLA	Wang, Jiacheng,et al."Exponential Stabilization of the Wave Equation on Hyperbolic Spaces with Nonlinear Locally Distributed Damping".APPLIED MATHEMATICS AND OPTIMIZATION (2021):13.