KMS Of Academy of mathematics and systems sciences, CAS
Dynamics of nonlinear hyperbolic equations of Kirchhoff type | |
Chen, Jianyi1; Sun, Yimin2; Xiu, Zonghu1; Zhang, Zhitao3,4,5 | |
2022-06-01 | |
Source Publication | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS |
ISSN | 0944-2669 |
Volume | 61Issue:3Pages:43 |
Abstract | 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 |
Indexed By | SCI |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000785750800004 |
Publisher | SPRINGER HEIDELBERG |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60373 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Zhang, Zhitao |
Affiliation | 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 |
Recommended Citation 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. |
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