|本期目录/Table of Contents|

[1]杨姗姗,蒋红标.一类半线性波动方程Cauchy问题破裂的新证法[J].浙江理工大学学报,2020,43-44(自科三):368-372.
 RAN Lixia,CHEN Yong.Large deviation principle of stochastically  modified CamassaHolm equation[J].Journal of Zhejiang Sci-Tech University,2020,43-44(自科三):368-372.
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一类半线性波动方程Cauchy问题破裂的新证法()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第43-44卷
期数:
2020年自科三期
页码:
368-372
栏目:
出版日期:
2020-06-09

文章信息/Info

Title:
Large deviation principle of stochastically  modified CamassaHolm equation
文章编号:
1673-3851 (2020) 03-0373-07
作者:
杨姗姗蒋红标
1.浙江理工大学 理学院,杭州 310018;2.丽水学院工学院,丽水 323000
Author(s):
RAN Lixia CHEN Yong
School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
半线性波动方程破裂能量解生命跨度试探函数
分类号:
O211-63
文献标志码:
A
摘要:
研究n维空间中带导数非线性项的半线性波动方程小初值Cauchy问题(Glassey猜想),证明当1<p≤1+2n-1(p为非线性指标)时,能量解将在有限时间破裂,并进一步建立了破裂解的生命跨度上界估计。在证明过程中,利用截断函数和线性波动方程的一个特殊解,构造了一个自身为负但其关于时间的一阶导数为非负的试探函数,用一种简洁明了的新方法得到了结论,简化了前人的证明。

参考文献/References:

[1] Glassey R. Mathematical reviews to “Global behavior of solutions to nonlinear wave equations in three space dimensions”. (1985-02-13)[2019-10-31].
[2] John F. Blowup for quasilinear wave equations in three space dimensions[J]. Communications on Pure and Applied Mathematics, 1981, 34(1): 29-51.
[3] Masuda K. Blowup of solutions for quasilinear wave equations in two space dimensions[M]//NorthHolland Mathematics Studies. Elsevier, 1984: 87-91. (2008-04-25)[2019-10-31].
[4] Schaeffer J. Finitetime blowup for u tt-△u=H(ur,ut) in two space dimensions[J]. Communications in Partial Differential Equations, 1986, 11(5): 513-543.
[5] John F. Nonexistence of global solutions of □u=tF(ut) in two and three space dimensions[J]. Rend.circ.mat.palermo Suppl, 1985(8):229-249.
[6] Agemi R. Blowup of solutions to nonlinear wave equations in two space dimensions[J]. Manuscripta Mathematica, 1991, 73(1): 153-162.
[7] Rammaha M A. Finitetime blowup for nonlinear wave equations in high dimensions[J]. Communications in Partial Differential Equations, 1987, 12(6): 677-700.
[8] Zhou Y. Blow up of solutions to the Cauchy problem for nonlinear wave equations[J]. Chinese Annals of Mathematics,2001, 22(3):275-280.
[9] Sideris T C. Global behavior of solutions to nonlinear wave equations in three dimensions[J]. Communications in Partial Differential Equations, 1983, 8(12): 1291-1323.
[10] Hidano K, Tsutaya K. Global existence and asymptotic behavior of solutions for nonlinear wave equations[J]. Indiana University Mathematics Journal, 1995, 44(4): 1273-1306.

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备注/Memo

备注/Memo:
收稿日期:2019-12-03
网络出版日期:2020-04-02
基金项目:国家自然科学基金项目(11401532);浙江省自然科学基金项目(LY18A010027)
作者简介:冉丽霞(1993-),女,甘肃陇南人,硕士研究生,主要从事随机偏微分方程方面的研究
通信作者:陈涌,E-mail:chenyong@zstu.edu.cn
更新日期/Last Update: 2020-06-10