Convergence rates in homogenization of higher order parabolic systems

TL;DR

This paper establishes the optimal convergence rate of order O(ε) in homogenization for higher order parabolic systems with oscillating coefficients, using duality arguments to improve understanding of solution behavior.

Contribution

It provides the first sharp O(ε) convergence rate in L^2(0,T; H^{m-1}(Ω)) for such systems, extending homogenization theory to higher order parabolic equations.

Findings

Achieved sharp O(ε) convergence rate in homogenization

Applied duality argument to improve convergence analysis

Validated results for both Dirichlet and Neumann boundary conditions

Abstract

This paper is concerned with the optimal convergence rate in homogenization of higher order parabolic systems with bounded measurable, rapidly oscillating periodic coefficients. The sharp $O(\va)$ convergence rate in the space $L^2(0,T; H^{m-1}(\Om))$ is obtained for both the initial-Dirichlet problem and the initial-Neumann problem. The duality argument inspired by \cite{suslinaD2013} is used here.