Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity

doi:10.1088/0951-7715/19/11/008

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	Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity
	Sun, Chunyou ; Cao, Daomin; Duan, Jinqiao
	2006-11-01
发表期刊	NONLINEARITY
ISSN	0951-7715
卷号	19 期号:11 页码:2645-2665
摘要	The authors consider non-autonomous dynamical behaviour of wave-type evolutionary equations with nonlinear damping and critical nonlinearity. These type of waves equations are formulated as non-autonomous dynamical systems (namely, cocycles). A sufficient and necessary condition for the existence of pullback attractors is established for norm-to-weak continuous non-autonomous dynamical systems, in terms of pullback asymptotic compactness or pullback kappa-contraction criteria. A technical method for verifying pullback asymptotic compactness via contractive functions is devised. These results are then applied to the wave-type evolutionary equations with nonlinear damping and critical nonlinearity, to obtain the existence of pullback attractors. The required pullback asymptotic compactness for the existence of pullback attractors is fulfilled by some new a priori estimates for concrete wave-type equations arising from applications. Moreover, the pullback kappa-contraction criterion for the existence of pullback attractors is of independent interest.
DOI	10.1088/0951-7715/19/11/008
语种	英语
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000241767400008
出版者	IOP PUBLISHING LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2594
专题	应用数学研究所
通讯作者	Sun, Chunyou
作者单位	1.Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China 2.Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China 3.IIT, Dept Appl Math, Chicago, IL 60616 USA
推荐引用方式 GB/T 7714	Sun, Chunyou,Cao, Daomin,Duan, Jinqiao. Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity[J]. NONLINEARITY,2006,19(11):2645-2665.
APA	Sun, Chunyou,Cao, Daomin,&Duan, Jinqiao.(2006).Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity.NONLINEARITY,19(11),2645-2665.
MLA	Sun, Chunyou,et al."Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity".NONLINEARITY 19.11(2006):2645-2665.