Attractors for a von Karman equation with memory

Abstract

In this paper a von Karman equation with memory, $$u_{tt} + \alpha \Delta ^2 u - \gamma \Delta u_{tt} - \int_{ - \infty }^t {\mu (t - s)} \Delta ^2 u(s)ds = [u,F(u)] + h$$ is considered. This equation was considered by several authors. Existing results are mainly devoted to global existence and energy decay. However, the existence of attractors has not yet been considered. Thus, we prove the existence and uniqueness of solutions by using Galerkin method, and then show the existence of a finite-dimensional global attractor.