UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS GENERALIZED 2D PARABOLIC EQUATIONS
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This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation −△ut + α2△2ut + μ△2u + ∇ · 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 is shown that the pullback attractor {Aǫ(t)}t∈R of the equation with ǫ > 0 converges to the global attractor A of the equation with ǫ = 0.
Abstract
This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation −△ut + α2△2ut + μ△2u + ∇ · 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 is shown that the pullback attractor {Aǫ(t)}t∈R of the equation with ǫ > 0 converges to the global attractor A of the equation with ǫ = 0.
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