Sami Loucif, Rafik Guefaifia, Salah Zitouni, Abdelouaheb Ardjouni

Well-Posedness and Exponential Decay for Piezoelectric Beams with Distributed Delay Term

In this paper, we consider a one-dimensional system of piezoelectric beams with distributed delay in the mechanical equation. We first prove the well-posedness of the system by using the semigroup theory. Next, we find the energy expression related to this system, and by using the technique of Lyapunov functional, we demonstrate that this system is exponentially stable and is independent of any coefficient of the system.

Mathematics Subject Classification: 35B40, 35B35

Key words and phrases: Piezoelectric beams, distributed delay, semigroup theory, energy expression, Lyapunov functional, exponential stability