Chapter 3 consider the initial - boundary value problem utt - where q is a bounded demain in rn with smooth boundary 3q ; with m ( s ) is a nonnegative c1 - function for s > 0 satisfying with we show that under certain conditions the solution blow up in finite time . chapter 4 consider the initial - boundary value problem and < ? > 2 . we show the decay rate of the solutions of the equation 第三章我们考虑了定义在具有光滑边界的有界区域上的kirchhoff型方程初边值问题其中0 ， r ， p 1 ， q 1 ， 1 ；当s 0时， m ( s )是空间c ~ 1中的非负函数，且满足其中， 0 ， 2这章我们给出了上述方程解的有限时刻爆破条件。
