Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains

In a thin heterogeneous porous layer, we carry out a multiscale analysis of Smoluchowski’s discrete diffusion–coagulation equations describing the evolution density of diffusing particles that are subject to coagulation in pairs. Assuming that the thin heterogeneous layer is made up of microstructures that are uniformly distributed inside, we obtain in the limit an upscaled model in the lower space dimension. We also prove a corrector-type result very useful in numerical computations. In view of the thin structure of the domain, we appeal to a concept of two-scale convergence adapted to thin heterogeneous media to achieve our goal.