Quantitative Homogenization of Attractors of Non-Newtonian Filtration Equations

Abstract

For a rapidly spatially oscillating nonlinearity g we compare solutions u(is an element of) of non-Newtonian filtration equation partial derivative(t)beta(u(is an element of)) - D(vertical bar Du(is an element of)vertical bar p-2Du(is an element of) + psi(u(is an element of))Du(is an element of)) + g(x, x/is an element of, u(is an element of)) = f(x, x/is an element of) with solutions u(0) of the homogenized, spatially averaged equation. partial derivative(t)beta(u(0)) - D(vertical bar Du(0)vertical bar(p-2) Du(0) + psi(u(0))Du(0)) + g(0) (x, u(0)) = f(0)(x). Based on an epsilon-independent a priori estimate, we prove that parallel to beta(u(epsilon))-beta(u(0))parallel to T,1 (Omega) <= Cee(rho t) uniformly for all t >= 0. Besides, we give explicit estimate for the distance between the nonhomogenized A(epsilon) and the homogenized A(0) attractors in terms of the parameter epsilon; precisely, we show fractional-order semicontinuity of the global attractors for epsilon SE arrow 0 : dist(L1(Omega)) (A(epsilon), A(0)) <= C epsilon gamma