Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems
Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems
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DOI：
10.1016/j.jde.2016.01.032
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发表时间：
2016-05-05
影响因子：
2.4
通讯作者：
Fukao, Takeshi
中科院分区：
文献类型：
--
作者：
Colli, Pierluigi;Fukao, Takeshi
研究了一类Cahn-Hilliard系统的渐近极限，得到了一般的非线性扩散方程.目标扩散方程可以再现许多著名的模型方程：Stefan问题、多孔介质方程、Hele-Shaw剖面、奇异对数型非线性扩散、Penrose-Fife型非线性扩散、快速扩散方程等，即通过设置Cahn-Hilliard系统的适当位势，所有这些问题都可以作为Cahn-Hilliard相关问题的极限而得到.证明了收敛性结果和误差估计。(C)2016 Elsevier Inc. All rights reserved.
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. (C) 2016 Elsevier Inc. All rights reserved.