on a bounded smooth domain Ω in md5=1409285b255bbc155b3cf510936386d6" title="Click to view the MathML source">Rn, md5=dd58b60303ca9359a6219eef7330769a" title="Click to view the MathML source">n≥1 with a homogeneous Neumann boundary condition, where the exponent md5=f99a7a442b68bb782a7b433f1aa910c2"> satisfies md5=25c81e04e34e77882857042a6c3ebbe1" title="Click to view the MathML source">p− := md5=c2e10304e3b1c9786693b573ab9bfbe8" title="Click to view the MathML source">minp(x)>2. We prove the existence of a pullback attractor and study the asymptotic upper semicontinuity of the elements of the pullback attractor md5=bcdca4f5d89991204805333e3a7988e9" title="Click to view the MathML source">A={A(t):t∈R} as md5=8d39b0a75c6c1580f98e0a231b40265b" title="Click to view the MathML source">t→∞ for the non-autonomous evolution inclusion in a Hilbert space H under the assumptions, amongst others, that F is a measurable multifunction and md5=a8ce5998a47a07098c08992361c049b4" title="Click to view the MathML source">D∈L∞([τ,T]×Ω) is bounded above and below and is monotonically nonincreasing in time. The global existence of solutions is obtained through results of Papageorgiou and Papalini.