Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 77, pp. 1-13.

Title: Pullback attractors for a singularly nonautonomous plate equation
       
Authors: Vera Lucia Carbone  (Univ. Federal de Sao Carlos, Brazil)
         Marcelo Jose Dias Nascimento (Univ. Federal de Sao Carlos, Brazil)
         Karina Schiabel-Silva  (Univ. Federal de Sao Carlos, Brazil)
	 Ricardo Parreira da Silva (IGCE-UNESP, Rio Claro, Brazil)

Abstract: 
 We consider the family of singularly nonautonomous plate  equations
 with structural damping
 $$
 u_{tt} + a(t,x)u_t - \Delta u_t + (-\Delta)^2 u
 + \lambda u = f(u),
 $$
 in a bounded domain $\Omega \subset \mathbb{R}^n$, with Navier boundary
 conditions. When the nonlinearity f is dissipative we show that
 this problem is globally well posed in
 $H^2_0(\Omega) \times L^2(\Omega)$ and has a family of
 pullback attractors which is upper-semicontinuous under small
 perturbations of the damping a.

Submitted January 14, 2011. Published June 20, 2011.
Math Subject Classifications: 35B41, 35L25, 35Q35.
Key Words: Pullback attractor; nonautonomous system;
           plate equation; upper-semicontinuity.