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浙江大学学报（理学版）
浙江大学学报（理学版）  2018, Vol. 45 Issue (4): 400-404    DOI: 10.3785/j.issn.1008-9497.2018.04.003
数学与计算机科学     
临界半线性波动方程解的有限时间破裂
汪海航1, 蒋红标2
1. 浙江理工大学 理学院, 浙江 杭州 310018;
2. 丽水学院 工学院, 浙江 丽水 323000
Finite time blow up for solutions of critical semilinear wave equations.
WANG Haihang1, JIANG Hongbiao2
1. School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China;
2. Institute of Engineering and Design, Lishui University, Lishui 323000, Zhejiang Province, China
 全文: PDF(975 KB)   HTML  
摘要： 研究了带临界指标的半线性波动方程utt-Δu=（1+|x|2）α|u|p小初值Cauchy问题解的破裂，证明了该问题在p=pc（n）时不存在整体解.
关键词： 半线性波动方程;  Cauchy问题;  临界指标;  破裂    
Abstract: This paper is devoted to study the Cauchy problems of critical semilinear wave equations, i.e. utt-Δu=(1+|x|2)α|u|p in high space dimensions(n ≥ 5), and establishes the blow-up result for the Cauchy problems with critical exponent p=pc(n).
Key words: semilinear wave equations    Cauchy problems    critical exponent    blow-up
收稿日期: 2017-08-10 出版日期: 2018-07-12
CLC:  O175.2  
基金资助: 浙江省自然科学基金资助项目（LY18A010008，LY14A010005）；浙江省一流学科项目（B类201601）；丽水市高层次人才项目（2016RC25）.
通讯作者: 蒋红标,通信作者,ORCID:http://orcid-org/0000-0003-2169-178X,E-mail:hbj@126.com.     E-mail: hbj@126.com
作者简介: 汪海航(1993-),ORCID:http://orcid.org/0000-0001-8406-9897,男,硕士,主要从事偏微分方程研究,E-mail:1196443777@qq.com.
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引用本文:

汪海航, 蒋红标. 临界半线性波动方程解的有限时间破裂[J]. 浙江大学学报（理学版）, 2018, 45(4): 400-404.

WANG Haihang, JIANG Hongbiao. Finite time blow up for solutions of critical semilinear wave equations.. Journal of Zhejiang University (Science Edition), 2018, 45(4): 400-404.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2018.04.003    或    https://www.zjujournals.com/sci/CN/Y2018/V45/I4/400

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