Reaction–Diffusion Equation on Thin Porous Media

Abstract

We consider a reaction–diffusion equation on a 3D thin porous media of thickness which is perforated by periodically distributed cylinders of size . On the boundary of the cylinders, we prescribe a dynamical boundary condition of pure-reactive type. As , in the 2D limit the resulting reaction–diffusion equation has a source term coming from the dynamical-type boundary conditions imposed on boundaries of the original 3D domain.