# Homogenization of monotone parabolic problems with an arbitrary number of spatial and temporal scales

## TL;DR

This paper establishes a general homogenization framework for monotone parabolic equations involving multiple spatial and temporal scales, extending previous results to more complex and arbitrary scale functions.

## Contribution

It introduces a homogenization result applicable to problems with arbitrary microscopic scales in space and time, using advanced multiscale convergence techniques.

## Key findings

- Proves a general homogenization theorem for complex multiscale parabolic problems.
- Extends homogenization theory to arbitrary scale functions beyond power laws.
- Provides an example illustrating the application of the main result.

## Abstract

In this paper we prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of epsilon. The main tools for the homogenization procedure are multiscale convergence and very weak multiscale convergence, both adapted to evo lution problems. At the end of the paper an example is given to concretize the use of the main result.