Reiterated Periodic Homogenization of Parabolic Monotone Operators with Nonstandard Growth

TL;DR

This paper develops a homogenization approach for parabolic problems with nonstandard growth operators in Orlicz spaces, using reiterated two-scale convergence to derive global and macroscopic homogenized models.

Contribution

It introduces a homogenization framework for parabolic monotone operators with nonstandard growth, extending the two-scale convergence method to Orlicz spaces.

Findings

Derivation of global homogenized problem

Derivation of macroscopic homogenized problem

Extension of two-scale convergence to Orlicz spaces

Abstract

In this paper, we are interested in reiterated periodic homogenization for a family of parabolic problems with nonstandard growth monotone operators leading to Orlicz spaces. The aim of this work is the determination of the global homogenized problem on the one hand and the macroscopic homogenized problem on the other hand, via the reiterated two-scale convergence method adapted to this type of spaces.