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.

Abstract

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 t≥0. 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 ϵ↘0:distL1(Ω)(Aϵ,A0)≤Cϵγ.