Pullback attractors for a singularly nonautonomous plate equation

Abstract

We consider the family of singularly nonautonomous plate equation with structural damping \[ u_{tt} + a(t,x)u_{t} + (- Δ) u_{t} + (-Δ)^{2} u + λu = f(u), \] 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 $H_0^2(\Omega )\times L^2(\Omega )$ and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping $a$.