Electron. J. Differential Equations, Vol. 2022 (2022), No. 70, pp. 1-13.

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

Shaohua Chen, Runzhang Xu, Chao Yang

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
DOI: https://doi.org/10.58997/ejde.2022.70

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Shaohua Chen
School of Science and Technology
Cape Breton University
Sydney, Nova Scotia B1P 6L2, Canada
email: george_chen@cbu.ca
Runzhang Xu
College of Mathematical Sciences
Harbin Engineering University
Harbin 150001, China
email: xurunzh@163.com; xurunzh@hrbeu.edu.cn
Chao Yang
College of Mathematical Sciences
Harbin Engineering University
Harbin 150001, China
email: yangchao_yc98@163.com; yangchao_@hrbeu.edu.cn

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