Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems

Pierluigi Colli; Takeshi Fukao

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arXiv · 1511.08853

Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems

Pierluigi Colli·Takeshi Fukao

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Abstract

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.

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Pierluigi Colli, Takeshi Fukao. 2015-11-27. Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems. https://arxiv.org/abs/1511.08853

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