Multiscale Modeling &Simulation, Volume 19, Issue 3, Page 1143-1166, January 2021.
Cahn--Hilliard models are central for describing the evolution of interfaces in phase separation processes and free boundary problems. In general, they have nonconstant and often degenerate mobilities. However, in the latter case, the spontaneous appearance of points of vanishing mobility and their impact on the solution are not well understood. In this paper we develop a singular perturbation theory to identify a range of degeneracies for which the solution of the Cahn--Hilliard equation forms a singularity in infinite time. This analysis forms the basis for a rigorous sharp interface theory and enables the systematic development of robust numerical methods for this family of model equations.

中文翻译：

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简并迁移率如何确定 Cahn-Hilliard 方程中的奇点形成？

多尺度建模与仿真，第 19 卷，第 3 期，第 1143-1166 页，2021
年1 月。Cahn--Hilliard 模型是描述相分离过程和自由边界问题中界面演化的核心。一般而言，它们具有非恒定且经常退化的流动性。然而，在后一种情况下，移动性消失点的自发出现及其对解决方案的影响尚不清楚。在本文中，我们开发了一种奇异微扰理论来确定一系列退化，对于这些退化，Cahn-Hilliard 方程的解在无限时间内形成奇点。这种分析构成了严格的锐界面理论的基础，并能够为该系列模型方程系统地开发稳健的数值方法。