Weak Solutions to the Degenerate Viscous Cahn-Hilliard Equation

The Cahn--Hilliard equation is a common model to describe phase separation processes of a mixture of two components. In this paper, we study the viscous Cahn--Hilliard equation with degenerate phase-dependent mobility. We define a notion of weak solutions and prove the existence of such weak solutions by considering the limits of the viscous Cahn--Hilliard equation with positive mobility. Also, we prove that such weak solutions satisfy an energy dissipation inequality under some additional conditions.