Parabolic Homogenization with an Interface

Abstract

This paper considers a family of second-order parabolic equations in divergence form with rapidly oscillating and time-dependent periodic coefficients and an interface between two periodic structures. Following a framework initiated by Blanc, Le Bris and Lions and a generalized two-scale expansion in divergence form of elliptic homogenization with an interface by Josien, we can determine the effective (or homogenized) equation with the coefficient matrix being piecewise constant and discontinuous across the interface. Moreover, we obtain the $O(\epsilon )$ convergence rates in $L_{x,t}^{2(d+2)/d}$ with $\epsilon$-smoothing method and the uniform interior Lipschitz estimates via compactness argument.

We change the title and fix some typos

References in corpus (2)

• Homogenization of locally periodic parabolic operators with non-self-similar scales
• Quantitative Estimates in Elliptic Homogenization of Non-divergence Form with Unbounded Drift and an Interface