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.