Dynamics of nonlinear hyperbolic equations of Kirchhoff type

doi:10.1007/s00526-022-02225-4

	Dynamics of nonlinear hyperbolic equations of Kirchhoff type
	Chen, Jianyi 5; Sun, Yimin 4; Xiu, Zonghu 5; Zhang, Zhitao 1,2,3
刊名	CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
	2022-06-01
卷号	61 期号:3 页码:43
ISSN号	0944-2669
DOI	10.1007/s00526-022-02225-4
英文摘要	In this paper, we study the initial boundary value problem of the important hyperbolic Kirchhoff equation u(tt) - (a integral(Omega) vertical bar del u vertical bar(2)dx + b) Delta u = lambda u + vertical bar u vertical bar(p-1)u, where a, b > 0, p > 1, lambda is an element of R and the initial energy is arbitrarily large. We prove several new theorems on the dynamics such as the boundedness or finite time blow-up of solution under the different range of a, b, lambda and the initial data for the following cases: (i) 1 < p < 3, (ii) p = 3 and a > 1/Lambda, (iii) p = 3, a <= 1/Lambda and lambda < b lambda(1), (iv) p = 3, a < 1/Lambda and lambda > b lambda(1), (v) p > 3 and lambda <= b lambda(1), (vi) p > 3 and lambda > b lambda(1), where lambda(1) = inf {parallel to del u parallel to(2)(2): u is an element of H-0(1)(Omega) and parallel to u parallel to(2) = 1}, and Lambda = inf {parallel to del u parallel to(4)(2): u is an element of H-0(1)(Omega) and parallel to u parallel to(4) = 1}. Moreover, we prove the invariance of some stable and unstable sets of the solution for suitable a, b and lambda, and give the sufficient conditions of initial data to generate a vacuum region of the solution. Due to the nonlocal effect caused by the nonlocal integro-differential term, we show many interesting differences between the blow-up phenomenon of the problem for a > 0 and a = 0.
资助项目	National Natural Science Foundation of China[12031015,11701310] ; National Natural Science Foundation of China[11771428,12026217] ; Research Foundation for Advanced Talents of Qingdao Agricultural University[6631114328] ; Research Foundation for Advanced Talents of Qingdao Agricultural University[6631115047]
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000785750800004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60372]
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Zhitao
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, HLM, Beijing 100190, Peoples R China 3.Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Jiangsu, Peoples R China 4.Northwest Univ, Sch Math, Xian 710127, Peoples R China 5.Qingdao Agr Univ, Sci & Informat Coll, Qingdao 266109, Peoples R China
推荐引用方式 GB/T 7714	Chen, Jianyi,Sun, Yimin,Xiu, Zonghu,et al. Dynamics of nonlinear hyperbolic equations of Kirchhoff type[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS,2022,61(3):43.
APA	Chen, Jianyi,Sun, Yimin,Xiu, Zonghu,&Zhang, Zhitao.(2022).Dynamics of nonlinear hyperbolic equations of Kirchhoff type.CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS,61(3),43.
MLA	Chen, Jianyi,et al."Dynamics of nonlinear hyperbolic equations of Kirchhoff type".CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 61.3(2022):43.