Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems

作者：Colli Pierluigi; Fukao Takeshi^*

来源：Journal of Differential Equations, 2016, 260(9): 6930-6959.

DOI：10.1016/j.jde.2016.01.032

• Cahn-Hilliard system
• Stefan problem
• Porous media equation
• Hele-Shaw profile
• Fast diffusion equation

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 these problems can be obtained as limits of the Cahn-Hilliard related problems. Convergence results and error estimates are proved.

• 出版日期2016-5-5