Quantitative Homogenization of Attractors of Non‐Newtonian Filtration Equations
Emil Novruzov · Mathematical Problems in Engineering · 2010
For a rapidly spatially oscillating nonlinearitygwe compare solutionsuϵof non‐Newtonian filtration equation∂tβ(uϵ) −D(|Duϵ|p−2Duϵ+φ(uϵ)Duϵ) +g(x,x/ϵ,uϵ) =f(x,x/ϵ) with solutionsu0of the homogenized, spatially averaged equation∂tβ(u0) −D(|Du0|p−2Du0+φ(u0)Du0) +g0(x,u0) =f0(x). Based on anε‐independent a priori estimate, we prove that uniformly for allt≥ 0. Besides, we give explicit estimate for the distance between the nonhomogenizedAϵand the homogenizedA0attractors in terms of the parameterϵ; precisely, we show fractional‐order semicontinuity of the global attractors for .