Upper Semicontinuity of Pullback Attractors for the 3D Nonautonomous Benjamin-Bona-Mahony Equations

Abstract

We will study the upper semicontinuity of pullback attractors for the 3D nonautonomouss Benjamin-Bona-Mahony equations with external force perturbation terms. Under some regular assumptions, we can prove the pullback attractors𝒜ε(t)of equationut-Δut-νΔu+∇·F→(u)=ɛg(x,t),x∈Ω,converge to the global attractor𝒜of the above-mentioned equation withε=0for anyt∈ℝ.