Asymptotic stability and blow-up for the wave equation with degenerate nonlocal nonlinear damping and source terms

Abstract

This work is devoted to studying a wave equation with degenerate nonlocal nonlinear damping and source terms. By potential well theory, we show the asymptotic stability of energy in the presence of a degenerate damping of polynomial type when the initial energy is small. Also, we firstly derive some sufficient conditions on initial data which lead to finite time blow-up.

Keywords:

• Asymptotic stability
• blow-up
• degenerate nonlocal damping
• wave equation

AMS Classifications (2010):

• 35B40
• 35B44
• 35L20

Acknowledgments

The authors would like to thank the referee for his/her valuable comments that resulted in the present improved version of the article. This work was supported by National Natural Science Foundation of China (Nos.11601122, 11801145).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China (Nos.11601122, 11801145).