一类Kirchhoff型双曲方程在任意初始能量下的有限时刻爆破

Finite time blow up for a Kirchhoff-type hyperbolic problem with arbitrary initial energy

研究一类带有分数次算子的Kirchhoff型双曲方程的有限时刻爆破问题.找到了一个与势阱深度无关的有限时刻爆破条件并估计了爆破时间上界,进一步,得到了解在任意高初始能量下的有限时刻爆破结果.文中的主要结果扩展了已有的一些爆破结果.

In this paper,the finite time blow up of a Kirchhoff-type hyperbolic problem with fractional operator is investigated.A blow up condition independent of the depth of the potential well is found and the upper bound of the blow up time is given.Furthermore,the finite time blow up result of solutions with arbitrary high initial energy is obtained.The main results presented in this paper generalize the recent ones in the literature.