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

Abstract

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