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http://dx.doi.org/10.4134/JKMS.2015.52.6.1149

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

PARK, JONG YEOUL (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY)
PARK, SUN-HYE (CENTER FOR EDUCATION ACCREDITATION PUSAN NATIONAL UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.52, no.6, 2015 , pp. 1149-1159 More about this Journal
Abstract
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 ${\epsilon}=0$.
Keywords
upper semicontinuity; generalized parabolic system; pullback attractor;
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