Journal of the
Korean Mathematical Society JKMS

This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation $$ - \Delta u_t + \alpha^2 \Delta^2 u_t + \mu \Delta^2 u + \nabla \cdot \overrightarrow{F} ( u) + B(u,u) = \epsilon g(x,t). $$ Under some proper assumptions on the external force term $g$, the upper semicontinuity of pullback attractors is proved. More precisely, it is shown that the pullback attractor $\{ A_{\epsilon}(t) \}_{t\in {\mathbb R}}$ of the equation with $\epsilon >0$ converges to the global attractor $A$ of the equation with $\epsilon =0 .$

Keywords: upper semicontinuity, generalized parabolic system, pullback attractor

MSC numbers: 60H15, 35B40, 35B41