A note on p-Laplacian parabolic problems in R-n

Author(s)

Simsen, Jacson ^[1]

Affiliation

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

• Document type: Journal article
• Source: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 75, n. 18, p. 6620-6624, DEC 2012.
• Web of Science Citations: 6

Abstract

In this work we study the asymptotic behavior of parabolic p-Laplacian problems of the form partial derivative u(lambda)/partial derivative t - div(D-lambda vertical bar del u(lambda)vertical bar(p-2)del u(lambda)) + a vertical bar u(lambda)vertical bar(p-2)u(lambda) = B(u(lambda)) in L-2(R-n), where n >= 1, p > 2, D-lambda is an element of L-infinity(R-n), infinity > M >= D-lambda(x) >= sigma > 0 a.e. in R-n. lambda is an element of {[}10, infinity), B : L-2(Rn) L-2(R-n) is a globally Lipschitz map and a : R-n -> R is a non-negative continuous function. We prove, under suitable assumptions on a, the existence of a global attractor in L-2(R-n) for each positive finite diffusion coefficient and we show that the family of attractors behaves upper semicontinuously with respect to positive finite diffusion parameters. (C) 2012 Elsevier Ltd. All rights reserved. (AU)