Reiterated homogenization of hyperbolic-parabolic equations in domains with tiny holes

TL;DR

This paper investigates the homogenization of hyperbolic-parabolic equations in porous media with tiny, periodically distributed holes, deriving a limit problem using multi-scale convergence that simplifies analysis of complex microstructures.

Contribution

It introduces a homogenization framework for hyperbolic-parabolic equations in perforated domains with periodic structures, extending existing methods to new complex media.

Findings

Derived a homogenized limit problem on a fixed domain

Confirmed the applicability of multi-scale convergence for such problems

Showed the limit problem retains the original equation type

Abstract

This article studies the homogenization of hyperbolic-parabolic equations in porous media with tiny holes. We assume that the holes are periodically distributed and that the coefficients of the equations are periodic. Using the multi-scale convergence method, we derive a homogenization result whose limit problem is defined on a fixed domain and is of the same type as the problem with oscillating coefficients.