具广义非线性源的波动方程的高能爆破

数学物理学报 ›› 2018, Vol. 38 ›› Issue (6): 1239-1244.

• 论文 • 上一篇

具广义非线性源的波动方程的高能爆破

杨延冰^1,²,连伟³,黄少滨²,徐润章^1,*()

¹ 哈尔滨工程大学理学院哈尔滨 150001
² 哈尔滨工程大学计算机科学与技术学院哈尔滨 150001
³ 哈尔滨工程大学自动化学院哈尔滨 150001

收稿日期:2017-08-29 出版日期:2018-12-26 发布日期:2018-12-27
通讯作者: 徐润章 E-mail:xurunzh@163.com
基金资助:
国家自然科学基金(11471087);中国博士后科学基金(2013M540270);黑龙江省博士后基金(LBH-Z15036)

Finite Time Blow up of Solutions for Nonlinear Wave Equation with General Nonlinearity for Arbitrarily Positive Initial Energy

Yanbing Yang^1,²,Wei Lian³,Shaobin Huang²,Runzhang Xu^1,*()

¹ College of Science, Harbin Engineering University, Harbin 150001
² College of Computer Science and Technology, Harbin Engineering University, Harbin 150001
³ College of Automation, Harbin Engineering University, Harbin 150001

Received:2017-08-29 Online:2018-12-26 Published:2018-12-27
Contact: Runzhang Xu E-mail:xurunzh@163.com
Supported by:
the NSFC(11471087);the China Postdoctoral Science Foundation(2013M540270);the Heilongjiang Postdoctoral Foundation(LBH-Z15036)

摘要/Abstract

摘要：

研究一类具广义非线性源的非线性波动方程的初边值问题在高初始能级状态下解的有限时间爆破.利用经典的凹函数方法找到了导致该问题具任意正初始能级的解有限时间爆破的初值.

关键词: 波动方程, 高初始能级, 有限时间爆破, 广义非线性源

Abstract:

This paper investigates the finite time blow up of solutions for the initial boundary value problem of a class of some nonlinear wave equations with general nonlinearity at high initial energy level. By employing the classical concavity method, we establish some new sufficient conditions on initial data such that the solution with arbitrarily positive initial energy blows up in finite time.

Key words: Wave equation, High initial energy, Finite time blow up, General nonlinearity

中图分类号:

O175.29

杨延冰,连伟,黄少滨,徐润章. 具广义非线性源的波动方程的高能爆破[J]. 数学物理学报, 2018, 38(6): 1239-1244.

Yanbing Yang,Wei Lian,Shaobin Huang,Runzhang Xu. Finite Time Blow up of Solutions for Nonlinear Wave Equation with General Nonlinearity for Arbitrarily Positive Initial Energy[J]. Acta mathematica scientia,Series A, 2018, 38(6): 1239-1244.

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具广义非线性源的波动方程的高能爆破

Finite Time Blow up of Solutions for Nonlinear Wave Equation with General Nonlinearity for Arbitrarily Positive Initial Energy

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