Homogenization of Three Species Reaction Diffusion Equation in Perforated Domains

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.