  An asymptotic limit of a class of Cahn-Hilliard systems is investigated to
obtain a general nonlinear diffusion equation. The target diffusion equation
may reproduce a number of well-known model equations: Stefan problem, porous
media equation, Hele-Shaw profile, nonlinear diffusion of singular logarithmic
type, nonlinear diffusion of Penrose-Fife type, fast diffusion equation and so
on. Namely, by setting the suitable potential of the Cahn-Hilliard systems, all
of these problems can be obtained as limits of the Cahn-Hilliard related
problems. Convergence results and error estimates are proved.
