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An asymptotic limit of a class of Cahn-Hilliard systems is investigated toobtain a general nonlinear diffusion equation. The target diffusion equationmay reproduce a number of well-known model equations: Stefan problem, porousmedia equation, Hele-Shaw profile, nonlinear diffusion of singular logarithmictype, nonlinear diffusion of Penrose-Fife type, fast diffusion equation and soon. Namely, by setting the suitable potential of the Cahn-Hilliard systems, allof these problems can be obtained as limits of the Cahn-Hilliard relatedproblems. Convergence results and error estimates are proved.

Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems