This paper is devoted to the blowup phenomena for a class of fourth-order wave equation with nonlinear strain term. First, for the model equation with strain structure, we prove the finite time blowup of solution for the critical initial energy, i.e., $E\left(0\right)=d$. Then, the finite time blowup and the upper bound of the blowup time are established for the sup-critical initial energy, i.e., $E\left(0\right)>0$.

中文翻译：

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带有非线性应变项的四阶波动方程的临界和超临界初始能量有限时间爆炸现象

本文致力于一类带有非线性应变项的四阶波动方程的爆破现象。首先，对于具有应变结构的模型方程，我们证明了临界初始能量的解的有限时间爆炸，即$Ë（0）=d$。然后，建立了超临界初始能量的有限时间爆燃和爆燃时间的上限，即$Ë（0）>0$。