一类带有非线性阻尼项和源项的四阶波动方程整体解的存在性与不存在性  

Global Existence and Nonexistence of Solutions for A Class of Fourth Order Wave Equation with Nonlinear Damping and Source Terms

作　　者：狄华斐[1] 尚亚东[1,2] 

机构地区：[1]广州大学数学与信息科学学院,广州510006 [2]广东省教育厅数学与交叉科学重点实验室,广州510006

出　　处：《数学物理学报（A辑）》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

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.

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 

分 类 号：O175.4[理学—数学]