Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 173408, 25 pages
Research Article

Quantitative Homogenization of Attractors of Non-Newtonian Filtration Equations

Department of Mathematics, Hacettepe University, 06532 Beytepe, Turkey

Received 8 December 2009; Accepted 11 April 2010

Academic Editor: Saad A. Ragab

Copyright © 2010 Emil Novruzov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For a rapidly spatially oscillating nonlinearity g we compare solutions uϵ of non-Newtonian filtration equation tβ(uϵ)-D(|Duϵ|p-2Duϵ+φ(uϵ)Duϵ)+g(x,x/ϵ,uϵ)=f(x,x/ϵ) with solutions u0 of the homogenized, spatially averaged equation tβ(u0)-D(|Du0|p-2Du0+φ(u0)Du0)+g0(x,u0)=f0(x). Based on an ε-independent a priori estimate, we prove that ||β(uϵ)-β(u0)||L1(Ω)Cϵeρt uniformly for all t0. Besides, we give explicit estimate for the distance between the nonhomogenized Aϵ and the homogenized A0 attractors in terms of the parameter ϵ; precisely, we show fractional-order semicontinuity of the global attractors for ϵ0:distL1(Ω)(Aϵ,A0)Cϵγ.