Pullback attractors for a singularly nonautonomous plate equation

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 $H^2_0(Omega) imes L^2(Omega)$ and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.

Keywords

• Pullback attractor
• nonautonomous system
• plate equation
• upper-semicontinuity