Improved blowup time estimates for fourth-order damped wave equations with strain term and arbitrary positive initial energy

Abstract

We propose a new differential inequality that improve the upper bound of the blowup time estimate for nonlinear fourth-order damped wave equations with strain term and arbitrary positive initial energy. We also give two new initial conditions to expand the range of the initial data leading to the finite time blowup of solutions. We obtain a sharp result of finite time blowup for the special case of the new differential inequality.We illustrate our results with some simulations.