Convergence rate in periodic homogenization of higher-order parabolic systems revisited

Abstract

We consider the convergence rate in periodic homogenization of higher order parabolic systems with time-dependent coefficients. The sharp $ O(\varepsilon) $-order scaling invariant convergence rate in the space $L^{2}(0,T;W^{m-1,p_{0}}(\Omega))$, $p_{0}=\frac{2d}{d-1}$, is derived by the duality argument. This largely improves the corresponding result by Niu and Xu in Discrete Contin. Dynam. Systems. Series A 38(8): 4203--4229 (2018).