中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
首页 机构 成果 学者
  
  1. CAS IR Grid
  2. 数学与系统科学研究院
  3. 中国科学院数学与系统科学研究院
Dynamics of nonlinear hyperbolic equations of Kirchhoff type

文献类型：期刊论文

作者Chen, Jianyi5; Sun, Yimin4; Xiu, Zonghu5; Zhang, Zhitao1,2,3
刊名CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
出版日期2022-06-01
卷号61期号:3页码:43
ISSN号0944-2669
DOI10.1007/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
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.

入库方式： OAI收割

来源：数学与系统科学研究院

浏览0
下载0
收藏0
其他版本

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。