Global attractors for a class of viscoelastic plate equations with past history

Abstract

This paper is concerned with a class of viscoelastic plate equations with past history. We first transform the original initial-boundary value problem into an equivalent one by means of the history space framework. Then we use the perturbed energy method to establish a stabilizability estimate. By employing the gradient property and quasi-stability of the dynamical system, we obtain the existence of a global attractor with finite fractal dimension.

Keywords

• viscoelastic plate equations
• past history
• global attractors
• gradient dynamical system
• quasi-stability