Dynamics of nonlinear hyperbolic equations of Kirchhoff type

doi:10.1007/s00526-022-02225-4

CSpace

	Dynamics of nonlinear hyperbolic equations of Kirchhoff type
	Chen, Jianyi 1; Sun, Yimin 2; Xiu, Zonghu 1; Zhang, Zhitao 3,4,5
	2022-06-01
发表期刊	CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0944-2669
卷号	61 期号:3 页码:43
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.
DOI	10.1007/s00526-022-02225-4
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000785750800004
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60373
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.Qingdao Agr Univ, Sci & Informat Coll, Qingdao 266109, Peoples R China 2.Northwest Univ, Sch Math, Xian 710127, Peoples R China 3.Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Jiangsu, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, 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.