Reaction–Diffusion Equation on Thin Porous Media

We consider a reaction–diffusion equation on 3D thin porous media of thickness $$\varepsilon $$ which is perforated by periodically distributed cylinders size . On the boundary cylinders, we prescribe dynamical condition pure-reactive type. As \rightarrow 0$$ , in 2D limit resulting has source term coming from dynamical-type conditions imposed boundaries original domain.