|本期目录/Table of Contents|

[1]吴邦,马正义,金云娟.带诺伊曼边界条件的小初值耗散半线性波动方程外问题解的破裂及生命跨度估计[J].浙江理工大学学报,2017,37-38(自科4):563-568.
　WU Bang,MA Zhengyi,JIN Yunjuan.Blow up for Small Initial Data Dissipation Semilinear Wave Equation Exterior Problem Solution with Neumann Boundary Condition and Life Span Estimation[J].Journal of Zhejiang Sci-Tech University,2017,37-38(自科4):563-568.
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带诺伊曼边界条件的小初值耗散半线性波动方程外问题解的破裂及生命跨度估计()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第37-38卷
期数:
2017年自科4期
页码:
563-568
栏目:
出版日期:
2017-07-10

文章信息/Info

Title:
Blow up for Small Initial Data Dissipation Semilinear Wave Equation Exterior Problem Solution with Neumann Boundary Condition and Life Span Estimation
文章编号:
1673-3851 (2017) 04-0563-06
作者:
吴邦; 马正义; 金云娟
1.浙江理工大学理学院，杭州 310018；2.丽水学院工程与设计学院，浙江 丽水 323000
Author(s):
WU Bang;  MA Zhengyi;  JIN Yunjuan
1.School of Sciences, Zhejiang SciTech University, Hangzhou 310018, China;
2.Institute of Engineering and Design, Lishui University, Lishui 323000, China
关键词:
半线性波动方程; 破裂; 初边值问题; 耗散; 生命跨度
分类号:
O175.29
文献标志码:
A
摘要:
运用试探函数研究了外区域上带诺伊曼边界条件的小初值耗散波动方程，证明：当非线性指数p满足1<p≤1+2N(N为空间维数)时解将在有限时内破裂；当1<p<1+2N时，得到了解的生命跨度上界估计。

参考文献/References:

［1］ NAKAO M, ONO K. Existence of global solutions to the cauchy problem for the semilinear dissipative wave equations［J］. Mathematische Zeitschrift,1993,214(1):325-342.
［2］ LI T T, ZHOU Y. Breakdown of solutions to  u+ut=u 1+α ［J］. Discrete and Continuous Dynamical Systems 1,1995,503-520.
［3］ NISHIHARA K. Lp－Lq estimates of solutions to the damped wave equation in 3\|dimensional space and their application［J］. Mathematische Zeitschrift,2003,244(3):631-649.
［4］ TODOROVA G, YORDANOV Y. Critical exponent for a nonlinear wave equation with damping［J］. Journal of Differential Equations,2001,174:464-489.
［5］ FUJITA H. On the blowing up of solutions of the cauchy problem for u t =Δu+u1+α ［J］. Journal of the Faculty of Science, the University of Tokyo: Sect. 1 A, Mathematics,1966,13:109-124.
［6］ ZHANG Q S. A blowup result for a nonlinear wave equation with damping: The critical case［J］. Comptes Rendus De Lacademie Des Sciences,2001,333(2):109-114.
［7］ LAI N A, ZHOU Y. The sharp lifespan estimate for semilinear damped wave equation with Fujita critical power in high dimensions. (2017-02-23)［2017-04-02］. https://arxiv.org/abs/1702.07073?context=math.
［8］ LAI N A, TAKAMURA H, WAKASA K. Blowup for semilinear wave equations with the scale invariant damping and super Fujita exponent

相似文献/References:

[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.
　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4):368.

备注/Memo

备注/Memo:
收稿日期： 2017-01-04
网络出版日期： 2017-06-21
基金项目： 浙江省自然科学基金项目(LY14A010005,LQ13A010013)
作者简介： 吴邦(1993-)，男，河南商丘人，硕士研究生，主要从事偏微分方程方面的研究
通信作者： 马正义，E\|mail:ma\|zhengyi@163.com
更新日期/Last Update: 2017-09-25