Nonlinear damping piezoelectric beams with past history, thermal and magnetic effects

H. Messaoudi, A. Ardjouni, S. Zitouni, H. E. Khochemane

In this study, we consider the one-dimensional system of piezoelectric beams with thermal and magnetic effects in the presence of a nonlinear damping term and with infinite history acting on the mechanical equation. Under suitable assumptions on the nonlinear damping term and the kernel, we demonstrate the existence and uniqueness of the solution applying the semigroup theory more precisely by Hille-Yosida theorem. And by introducing a suitable Lyapunov functional and using some properties of convex functions, we show the general stability for the system which the exponential and polynomial decays are merely special cases. Furthermore, our results are independent of any relationship between system parameters. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 17(1) (2024), pp. 71-94