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

Title & Authors
UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS GENERALIZED 2D PARABOLIC EQUATIONS
PARK, JONG YEOUL; PARK, SUN-HYE;

Abstract
This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation $\small{-{\Delta}u_t+{\alpha}^2{\Delta}^2u_t+{\mu}{\Delta}^2u+{\bigtriangledown}{\cdot}{\vec{F}}(u)+B(u,u)={\epsilon}g(x,t)}$. 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 $\small{\{A_{\epsilon}(t)\}_{t{\epsilon}{\mathbb{R}}}}$ of the equation with $\small{{\epsilon}}$>$\small{0}$ converges to the global attractor A of the equation with $\small{{\epsilon}=0}$.
Keywords
upper semicontinuity;generalized parabolic system;pullback attractor;
Language
English
Cited by
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