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

doi:10.1007/s00245-021-09751-1

	Exponential Stabilization of the Wave Equation on Hyperbolic Spaces with Nonlinear Locally Distributed Damping
	Wang, Jiacheng 2,3; Ning, Zhen-Hu 1; Yang, Fengyan 4
刊名	APPLIED MATHEMATICS AND OPTIMIZATION
	2021-01-30
页码	13
关键词	Wave equation Stabilization Hyperbolic spaces Nonlinear locally distributed damping
ISSN号	0095-4616
DOI	10.1007/s00245-021-09751-1
英文摘要	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.
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
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000613037600001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58091]
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.Beijing Univ Technol, Fac Informat Technol, Beijing 100124, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, 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.