Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 70, pp. 1-13.

Title: Improved blowup time estimates for fourth-order damped wave equations with 
       strain term and arbitrary positive initial energy
       
Authors: Shaohua Chen (Cape Breton Univ., Sydney, Nova Scotia, Canada)
         Runzhang Xu (Harbin Engineering Univ., Harbin, China)
         Chao Yang   (Harbin Engineering Univ., Harbin, China)

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.

Submitted May 22, 2022. Published October 12, 2022.
Math Subject Classifications: 35L35, 35B44, 35L05, 35D30.
Key Words: Finite time blowup; fourth-order wave equation; strain term;
           arbitrary positive initial energy