  Condition imposed on the nonlinear terms of a nonlinear diffusion equation
with {R}obin boundary condition is the main focus of this paper. The degenerate
parabolic equations, such as the {S}tefan problem, the {H}ele--{S}haw problem,
the porous medium equation and the fast diffusion equation, are included in
this class. By characterizing this class of equations as an asymptotic limit of
the {C}ahn--{H}illiard systems, the growth condition of the nonlinear term can
be improved. In this paper, the existence and uniqueness of the solution are
proved. From the physical view point, it is natural that, the
{C}ahn--{H}illiard system is treated under the homogeneous {N}eumann boundary
condition. Therefore, the {C}ahn--{H}illiard system subject to the {R}obin
boundary condition looks like pointless. However, at some level of
approximation, it makes sense to characterize the nonlinear diffusion
equations.
