Existence and continuity of attractors for a nonlinear piezoelectric beam with Colemam-Gurtin thermal law

In this paper, we study the long-time dynamics of a nonlinear model piezoelectric beam subjected to magnetic and thermal effects. The effect acts on system according Coleman-Gurtin law. Using semigroup theory, prove existence uniqueness solutions. global attractors is proved by showing that dynamical associated with solutions quasi-stable gradient. To conclude, show family continuous dense residual set upper semicontinuous closed interval.