Homogenization of Three Species Reaction Diffusion Equation in Perforated Domains

TL;DR

This paper analyzes how microscale perforations influence the macroscale behavior of a three-species reaction-diffusion system, revealing that perforations induce a global source term in the homogenized model.

Contribution

It introduces a homogenization approach for three-species reaction-diffusion equations in perforated domains, highlighting the impact of microscale mass inflow on macroscale dynamics.

Findings

Perforations lead to a global source term in the homogenized equation.

The homogenized system retains the three-species structure with modified diffusion coefficients.

Microscale effects are captured via two-scale convergence techniques.

Abstract

In this article we study the asymptotic behaviour of the solution of the three species chemical reaction-diffusion model with non-homogeneous Neumann boundary condition in a perforated domain. We investigate how the mass inflow at the microscale affects the three-species reaction-diffusion system at the macroscale using two-scale convergence. As the size of the perforations vanishes, the microscale effects are captured by a global source term in the homogenized equation, which remains a three-species reaction-diffusion system but with modified diffusion coefficients.