Quantitative Homogenization of Attractors of Non-Newtonian Filtration Equations

الملخص EN

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.