Large-scale boundary estimates of parabolic homogenization over rough boundaries

In this paper, for a family of second-order parabolic system or equation with rapidly oscillating and time-dependent periodic coefficients over rough boundaries, we obtain the large-scale boundary estimates, by a quantitative approach. The quantitative approach relies on approximating twice: we first approximate the original parabolic problem over rough boundary by the same equation over a non-oscillating boundary and then approximate the oscillating equation over a non-oscillating boundary by its homogenized equation over the same non-oscillating boundary.