Pullback attractors for a singularly nonautonomous plate equation

We consider the family of singularly nonautonomous plate equation with structural damping [ u_{tt} + a(t,x)u_{t} + (- \Delta) u_{t} + (-\Delta)^{2} u

• \lambda u = f(u), ] in a bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^n$, with Navier boundary conditions. When the nonlinearity $f$ is dissipative we show that this problem is globally well posed in $H_0^2(\mathrm{\Omega })\times L^2(\mathrm{\Omega })$ and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping $a$.