任意正初始能量状态下半线性波动方程解的有限时间爆破

数学物理学报 ›› 2017, Vol. 37 ›› Issue (6): 1085-1093.

任意正初始能量状态下半线性波动方程解的有限时间爆破

苏晓¹, 王书彬²

1 河南工业大学理学院郑州 450001;
2 郑州大学数学与统计学院郑州 450001

收稿日期:2016-11-19 修回日期:2017-05-12 出版日期:2017-12-26 发布日期:2017-12-26
作者简介:王书彬,E-mail:wangshubin@zzu.edu.cn
基金资助:
国家自然科学基金（11171311）

Finite Time Blow-Up for the Damped Semilinear Wave Equations with Arbitrary Positive Initial Energy

Su Xiao¹, Wang Shubin²

1 College of Science, Henan University of Technology, Zhengzhou 450001;
2 School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001

Received:2016-11-19 Revised:2017-05-12 Online:2017-12-26 Published:2017-12-26
Supported by:
Supported by the NSFC (11171311)

摘要/Abstract

摘要： 研究了具有强阻尼的半线性波动方程的初边值问题.在一定的初值条件下，给出高初始能量状态下解在有限时间爆破的充分条件.另外在任意正初始能量状态下给出解在能量空间中整体存在的充分条件.

关键词: 阻尼波动方程, 高初始能量, 爆破, 整体解

Abstract: This paper investigates the initial-boundary value problem of the semilinear wave equation with strong damped terms. We provide the sufficient conditions of finite time blow-up of solutions with high initial energy under some reasonable restrictions on the initial data. In the case of the arbitrary positive initial energy, we also present the sufficient conditions of the existence of global solutions in the energy space.

Key words: Damped wave equations, High initial energy, Blow-up, Global existence

中图分类号:

O175

苏晓, 王书彬. 任意正初始能量状态下半线性波动方程解的有限时间爆破[J]. 数学物理学报, 2017, 37(6): 1085-1093.

Su Xiao, Wang Shubin. Finite Time Blow-Up for the Damped Semilinear Wave Equations with Arbitrary Positive Initial Energy[J]. Acta mathematica scientia,Series A, 2017, 37(6): 1085-1093.

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