Reaction-diffusion equation on thin porous media

Abstract

We consider a reaction-diffusion equation on a 3D thin porous media of thickness $\varepsilon$ which is perforated by periodically distributed cylinders of size $\varepsilon$. On the boundary of the cylinders we prescribe a dynamical boundary condition of pure-reactive type. As $\varepsilon\to 0$, 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.