动态边界条件下一类阻尼波动方程解的研究

STUDY FOR A CLASS OF DAMPED WAVE EQUATION WITH DYNAMIC BOUNDARY CONDITIONS

本文研究了一类动态边界条件下阻尼波动方程解的问题.利用位势井理论,通过构造稳定集和不稳定集,并结合能量分析的方法,获得了如下结果.首先,当初值属于稳定集时该问题存在整体解,且E(0)<d时其能量具有指数衰减速率;其次,当u0和E(0)满足一定条件时,该问题的解在Lp范数下以指数增长;最后,给出解在有限时间爆破的充分必要条件.

In this paper,we study the solution for a class of wave equation with damping terms and dynamic boundary conditions.Using the potential well method,by constructing stable and unstable sets,and combining energy method,we obtain the follows results.First,if the initial data are in the＂stable set＂,then the global solution is got,and if E（0）d,then the energy grows exponentially.Secondly,when u0 and E（0）satisfy certain conditions,the solution grows exponentially in Lp norm.Finally,the necessary and sufficient conditions are given for the solution blow up in finite time.