Reiterated homogenization of parabolic systems with several spatial and temporal scales

We consider quantitative estimates in the homogenization of second-order parabolic systems with periodic coefficients that oscillate on multiple spatial and temporal scales, partial differential t - div(A(x, t, x/epsilon 1, ... , x/epsilon n, t/epsilon i, ... , t/epsilon � ) backward difference ), m where epsilon t = epsilon alpha e, epsilon k = epsilon ssk, 2 = 1, ..., n, k = 1, ..., m, with 0 G alpha 1 G ... G alpha n G infinity and 0 G ss1 G ... G ssm G infinity. The convergence rate in the homogenization is derived in the L2 space, and the large-scale interior and boundary Lipschitz estimates are also established. In the case n = m = 1, such issues have been addressed by Geng and Shen (2020) [12] based on an interesting scale reduction technique developed therein. Our investigation relies on a quantitative reiterated homogenization theory. (c) 2024 Elsevier Inc. All rights reserved.