KMS Of Academy of mathematics and systems sciences, CAS
Exponential Stabilization of the Wave Equation on Hyperbolic Spaces with Nonlinear Locally Distributed Damping | |
Wang, Jiacheng1,2; Ning, Zhen-Hu3; Yang, Fengyan4 | |
2021-01-30 | |
Source Publication | APPLIED MATHEMATICS AND OPTIMIZATION |
ISSN | 0095-4616 |
Pages | 13 |
Abstract | 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. |
Keyword | Wave equation Stabilization Hyperbolic spaces Nonlinear locally distributed damping |
DOI | 10.1007/s00245-021-09751-1 |
Indexed By | SCI |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000613037600001 |
Publisher | SPRINGER |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58092 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Yang, Fengyan |
Affiliation | 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 |
Recommended Citation 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. |
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