Smoluchowski Equation with Variable Coefficients in Perforated Domains: Homogenization and Applications to Mathematical Models in Medicine

In this paper, we study the homogenization of a Smoluchowski system of periodic discrete diffusion-coagulation equations, when the diffusion coefficients depend on all variables, in particular on the microscopic variable. This system modelizes the aggregation and diffusion of the ˇ-amyloid peptide Abeta 42 in the cerebral tissue, a process associated with the development of Alzheimer’s disease. Our homogenization result, based on Allaire-Nguetseng two-scale convergence, is meant to pass from a microscopic model to a macroscopic one.