# Homogenization results for a coupled system of reaction-diffusion equations

## TL;DR

This paper derives homogenization results for a coupled reaction-diffusion system in periodic porous media, modeling complex biochemical processes in cells with nonlinear reactions affecting diffusion and source terms.

## Contribution

It provides new homogenization results for a coupled nonlinear PDE system modeling reaction-diffusion in porous media, capturing microscopic reactions' effects at the macroscopic level.

## Key findings

- Derivation of effective macroscopic equations from microscopic models.
- Identification of additional source/sink terms due to nonlinear reactions.
- Analysis of how microscopic reactions influence macroscopic diffusion properties.

## Abstract

The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying several metabolic processes taking place in living cells, in which biochemical species can diffuse in the cytosol and react both in the cytosol and also on the organellar membranes. The coupling of the concentrations of the biochemical species is realized via various properly scaled nonlinear reaction terms. These nonlinearities, which model, at the microscopic scale, various volume or surface reaction processes, give rise in the macroscopic model to different effects, such as the appearance of additional source or sink terms or of a non-standard diffusion matrix.