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

Author(s)

Simsen, Jacson ^[1] ; Nascimento, Marcelo J. D. ^[2] ; Simsen, Mariza S. ^[1]

Affiliation

^[1] Univ Fed Itajuba, Inst Matemat Comp, BR-37500903 Itajuba, MG - Brazil

^[2] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Paulo - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 413, n. 2, p. 685-699, MAY 15 2014.
• Web of Science Citations: 10

Abstract

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. (AU)

• FAPESP's process: 11/04166-5 - Continuity of attractors to parabolic problems
• Grantee: Marcelo José Dias Nascimento
• Support Opportunities: Regular Research Grants