English

Large-scale boundary estimates of parabolic homogenization over rough boundaries

Analysis of PDEs 2024-11-14 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2411.08362,
  title  = {Large-scale boundary estimates of parabolic homogenization over rough boundaries},
  author = {Pengxiu Yu and Yiping Zhang},
  journal= {arXiv preprint arXiv:2411.08362},
  year   = {2024}
}