Convergence rates in homogenization of parabolic systems with locally periodic coefficients

Abstract

In this paper we study the quantitative homogenization of second-order parabolic systems with locally periodic (in both space and time) coefficients. The O(ε) scale-invariant error estimate in L2(0,T;L2dd−1(Ω)) is established in C1,1 cylinders under minimum smoothness conditions on the coefficients. This process relies on critical estimates of smoothing operators. We also develop a new construction of flux correctors in the parabolic manner and a sharp estimate for temporal boundary layers.