Well-posedness and general energy decay for a nonlinear piezoelectric beams system with magnetic and thermal effects in the presence of distributed delay

Abstract

In this paper, we consider one-dimensional nonlinear piezoelectric beams with thermal and magnetic effects in the presence of a distributed delay term acting on the heat equation. First, we show that the system is well-posed in the sense of a semigroup. Through the construction of an appropriate Lyapunov functional, we establish a general decay result for the solutions of the system, for which the exponential and polynomial decays are only special cases, under a suitable assumption on the weight of the delay that the damping effect through heat conduction is strong enough to stabilize the system even in the presence of a time delay. Furthermore, our result does not depend on any relationship between system parameters.

Keywords:

• Distributed delay
• energy method
• general decay
• lyapunov functional
• nonlinear damping
• piezoelectric beams
• semigroup approach

2020 Mathematics Subject Classification:

• 35B40
• 35B35
• 35L05

Acknowledgements

The authors would like to thank the anonymous referee for his/her valuable comments and good advice.

Disclosure statement

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

Data availability statement

No data were used to support this study.