  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 a limit of an equation and dynamic boundary
condition of Cahn-Hilliard type. By using this Cahn-Hilliard approach, it
becomes clear that the state of the mushy region of the Stefan problem is
characterized by an asymptotic limit of the fourth-order system, which has a
double-well structure. This fact also raises the possibility of the numerical
application of the Cahn-Hilliard system to the degenerate parabolic equation,
of which the Stefan problem is one.
