Convergence of Cahn-Hilliard systems to the Stefan problem with dynamic boundary conditions

This paper examines the well-posedness of the Stefan problem with a dynamic boundary condition. To show the existence of the weak solution, the original problem is approximated by the limit of an equation and a dynamic boundary condition of Cahn-Hilliard-type. Using this Cahn-Hilliard approach, the enthalpy formulation of the Stefan problem is characterized by the asymptotic limit of a fourth-order system that has a double-well structure. The main result obtained for the Stefan problem can also be applied to a wider class of degenerate parabolic equations by setting the nonlinearity to give the general maximal monotone graph.