A Cahn-Hilliard model in bounded domains with permeable walls

In this article, we propose a model of phase separation in a binary mixture confined to a bounded region which may be contained within porous walls. The boundary conditions are derived from a mass conservation law and variational methods. Employing classical methods, that is, fixed point theorems and standard energy methods, we obtain the existence and uniqueness of a global solution to our problem. We then also compare our model of phase separation with other previous Cahn-Hilliard equations with homogeneous Neumann and dynamic boundary conditions.