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, ∂ t − div (A (x , t , x / ε 1 , ... , x / ε n , t / ε 1 ′ , ... , t / ε m ′) ∇) , where ε ℓ = ε α ℓ , ε k ′ = ε β k , ℓ = 1 ,... , n , k = 1 ,... , m , with 0 < α 1 <... < α n < ∞ and 0 < β 1 <... < β m < ∞. The convergence rate in the homogenization is derived in the L 2 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. [ABSTRACT FROM AUTHOR]