Existence and exponential decay of solutions for magnetic effected piezoelectric beams with delay terms

M. Douib, H. Messaoudi, S. Zitouni

In this work, we consider a one-dimensional piezoelectric beam model with magnetic effects in the presence of a delay term acting on the two equations. The existence and uniqueness of solutions to the system are proved by the semigroup theory. We demonstrate the system's exponential stability using the energy method and multiplier techniques. Under a suitable assumption on the weight of the delay that the damping effect through two equations 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. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 17(3) (2024), pp. 51-67