Global attractor for a nonlinear plate equation with supported boundary conditions

In this paper, we consider a two-dimensional nonlinear equation(∗) ρ w t t + D Δ 2 w + ε μ w t − ( N 1 + T 2 ∫ Ω w x 2 d x d y ) w x x − ( N 2 + T 2 ∫ Ω w y 2 d x d y ) w y y = 0 which arises from the model of the viscoelastic thin rectangular plate with four edges supported. By virtue of Galerkin method combined with the priori estimates, we prove the existence and uniqueness of the global solution under initial–boundary data for the above equation. Especially the existence of the bounded absorbing set in space E and the existence of the global attractor of system is also obtained.