摘要
考虑一类带有非线性阻尼项和源项的四阶波动方程的初边值问题.通过结合Galerkin逼近,势井方法和单调紧致方法,在最少的先验估计下获得了整体解的存在性.此外,在初始能量为负的情况下,证明了存在有限时间内爆破的解.
In this paper, we consider the initial boundary value problem of the fourth order wave equation with nonlinear damping and source terms. By the combination of Galerkin approximations, Potential well and Monotonicity-Compactness methods, the global existence of solutions is obtained with the least amount of a priori estimates. Moreover, we prove that there are solutions with negative initial energy that blow up in finite time.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2015年第3期618-633,共16页
Acta Mathematica Scientia
基金
国家自然科学基金(11401122
40890150)
广东省科技计划项目(2008B080701042)资助
关键词
波动方程
整体存在性
爆破
阻尼项和源项
单调紧致法
Wave equation
Global existence
Blow up
Damping and source terms
Monotonicity- Compactness methods.
