Longtime dynamics for a novel piezoelectric beam model with creep and thermo-viscoelastic effects

Abstract

In this work, a novel fully-dynamic piezoelectric beam model is considered. Electromagnetic and thermal effects are taken into consideration by Maxwell’s equations and the Coleman–Gurtin law (instead of the Fourier’s law), respectively. Our model accounts also for thermal and electromagnetic (creep) past histories, which are in line with the time response of PVDF at the applied stress in the longitudinal direction. Under suitable assumptions, the existence and uniqueness of solutions are proved by the semigroup theory. The main purpose of this paper is to establish the longtime dynamics of the model. Therefore, the quasi-stability property of the model and the existence of smooth global attractors with finite fractal dimension are obtained. The existence of exponential attractors for the associated dynamical system is also proved.