# Homogenization of linear parabolic equations with a certain resonant matching between rapid spatial and temporal oscillations in periodically perforated domains

## TL;DR

This paper investigates the homogenization process of linear parabolic equations with oscillating coefficients in perforated domains, focusing on the interplay between spatial and temporal oscillations and their effects on multiscale limits.

## Contribution

It introduces a novel analysis of homogenization in perforated domains with resonant spatial-temporal oscillations, including new multiscale convergence characterizations.

## Key findings

- Characterization of multiscale limits for gradients
- Development of very weak multiscale convergence methods
- Results applicable to homogenization in perforated domains

## Abstract

In this article, we study homogenization of a parabolic linear problem governed by a coefficient matrix with rapid spatial and temporal oscillations in periodically perforated domains with homogeneous Neumann data on the boundary of the holes. We prove results adapted to the problem for a characterization of multiscale limits for gradients and very weak multiscale convergence.