UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS GENERALIZED 2D PARABOLIC EQUATIONS

Abstract

Abstract. This paper is concerned with a generalized 2D parabolicequation with a nonautonomous perturbation−∆u t + α 2 ∆ 2 u t + µ∆ 2 u + ∇ ·→F (u) + B(u,u) = ǫg(x,t).Under some proper assumptions on the external force term g, the up-per semicontinuity of pullback attractors is proved. More precisely, it isshown that the pullback attractor {A ǫ (t)} t∈R of the equation with ǫ > 0converges to the global attractor A of the equation with ǫ = 0. 1. IntroductionThis work is concerned with the upper semicontinuity of pullback attractorsfor non-autonomous generalized 2D parabolic equations. Let Ω be a boundeddomain in R 2 with smooth boundary ∂Ω and (x 1 ,x 2 ) ∈ Ω. Consider a non-autonomous generalized 2D parabolic equation−∆u t +α 2 ∆ 2 u t +µ∆ 2 u+∇ ·→F (u)+B(u,u) = ǫg(x,t) in Ω ×[τ,∞),u =∂u∂ν(1.1) = 0 on ∂Ω×[τ,∞),u(x,τ) = u τ (x) in Ω,where ǫ is a small positive parameter, u t = ∂u∂t , α, µ are positive constants,→F is a nonlinear vector function, g is an external forcing term with g ∈L