Reaction-diffusion equation on thin porous media

Abstract

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

17 pages. arXiv admin note: text overlap with arXiv:1712.01183, arXiv:1912.02445

Cited by in corpus (2)

• On $p$-Laplacian reaction-diffusion problems with dynamical boundary conditions in perforated media
• Sharp pressure estimates for the Navier-Stokes system in thin porous media