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

This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation $$-{\Delta}u_t+{\alpha}^2{\Delta}^2u_t+{\mu}{\Delta}^2u+{\bigtriangledown}{\cdot}{\vec{F}}(u)+B(u,u)={\epsilon}g(x,t)$$. Under some proper assumptions on the external force term g, the upper semicontin...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 52; no. 6; pp. 1149 - 1159
Main Authors PARK, JONG YEOUL, PARK, SUN-HYE
Format Journal Article
LanguageKorean
Published 2015
Subjects
generalized parabolic system
upper semicontinuity
pullback attractor
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Summary:This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation $$-{\Delta}u_t+{\alpha}^2{\Delta}^2u_t+{\mu}{\Delta}^2u+{\bigtriangledown}{\cdot}{\vec{F}}(u)+B(u,u)={\epsilon}g(x,t)$$. 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 $\{A_{\epsilon}(t)\}_{t{\epsilon}{\mathbb{R}}}$ of the equation with ${\epsilon}>0$ converges to the global attractor A of the equation with ${\epsilon}=0$.
Bibliography:KISTI1.1003/JNL.JAKO201532434264233
ISSN:0304-9914