Stability of a viscoelastic Timoshenko system with non-monotonic kernel

Abstract

In this paper, the stability of a linear Timoshenko beam system involved with infinite memory is considered. Different from the previous results on where the monotony of kernel is always fulfilled, the memory kernel under consideration is assumed to be non-monotonic. The well-posedness of the system is obtained by means of resolvent family theory and the exponential stability is proved under certain conditions. Numerical simulations are also presented to verify the main results.

Keywords:

• Exponential stability
• Timoshenko system
• non-monotonic memory kernel

2000 AMS Subject Classifications:

• 35B40
• 93D05
• 93D23

Acknowledgments

The authors would like to appreciate the CE and referees for their helpful and valuable comments and suggestions.

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (NSFC) [grant numbers 61773277, 62073236].