Critical and sup-critical initial energy finite time blowup phenomena for the fourth-order wave equations with nonlinear strain term

Abstract

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(0)=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(0)>0.