A note on blow-up of solutions for a class of fourth-order wave equation with viscous damping term

Abstract

In this note, we study a class of fourth-order wave equation with viscous damping term and illuminate that the condition on the relationship between and p in Theorem 4.2 of Xu et al. (Appl Anal. 2013;92(7):1403–1416) can be removed. This is achieved by adopting and modifying the so-called concavity method. Furthermore, we establish a blow-up result for positive initial energy without the relationship between and p as well.

Keywords:

• Wave equation
• viscous damping term
• blow up
• positive initial energy

Acknowledgements

The authors express sincere thanks to the editors and anonymous reviewers for their constructive comments and suggestions that helped to improve this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11301277]; Natural Science Foundation of Jiangsu Province [grant number BK20151523]; Six Talent Peaks Project in Jiangsu Province [grant number 2015-XCL-020]; Qing Lan Project of Jiangsu Province.