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
Show me the PDF file (380 KB), TEX file for this article.
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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 |
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Runzhang Xu College of Mathematical Sciences Harbin Engineering University Harbin 150001, China email: xurunzh@163.com; xurunzh@hrbeu.edu.cn |
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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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