Homogenization of a nonlinear reaction‐diffusion problem in a perforated domain with different size obstacles

Abstract

In this paper we consider a nonlinear reaction‐diffusion problem with low diffusion scales of order in a porous domain which periodically perforated by two different size obstacles. A nonlinear Neumann condition is prescribed on the boundaries of smaller obstacles, while a homogeneous Neumann condition is imposed on the other boundaries. Our aim is to derive the homogenized model as the small parameters tend to zero by using the method of three‐scale convergence and periodic reiterated unfolding operator. The final homogenized macroscopic model depends on three scales.