Existence and upper semicontinuity of pullback attractors for non-autonomous p-Laplacian parabolic problems

We study the asymptotic behavior of parabolic p-Laplacian problems of the form partial derivative u/partial derivative (t) - div (DA (t) I nu x (t)1P-2VuA (t)) + I uA (t) IP-2uA (t) = B(t,uA(t)) ut in a bounded smooth domain Q in IV, where n 1, p> 2, DA E L'([T-1,1] x S-2) with 0 < DA(t,x) m a.e. in [7, T] x fl, A E [0, co) and for each A E [0, infinity) we have IDA (s,x) - DA (t,x)I CA Is - trA for all x E Q, s, t E [T, 71 for some positive constants 0A and CA. Moreover, DA DA in L-infinity([gamma,lambda 1 x 12) as -> Al. We prove that for each A E [0,00) the evolution process of this problem has a pullback attractor and we show that the family of pullback attractors behaves upper semicontinuously at lambda(i). (C) 2013 Elsevier Inc. All rights reserved.