Dynamics for a Viscoelastic Beam Equation With Past History and Nonlocal Boundary Dissipation

This article aims to study the long‐time dynamics of the linear viscoelastic plate equation subject to nonlinear and nonlocal boundary conditions. This model, with , was first considered by Cavalcanti [ Discrete and Continuous Dynamical Systems 8, no. 3 (2002): 675–695], where results of global existence and uniform decay rates of energy have been established. In this work, by taking , and considering the autonomous equivalent problem we prove that the dynamical system generated by the weak solutions has a compact global attractor (in the topology of the weak phase space ), which in subcritical case has finite dimension and smoothness. Furthermore, when the force follows the Hook Law , we prove that possesses a (generalized) fractal exponential attractor with finite dimension in a space .