In this paper, we consider a class of the degenerate Cahn–Hilliard equation with a smooth double-well potential. By applying a semi-discretization technique and asymptotic analysis method on non-degenerate Cahn–Hilliard equation, we obtain the existence and regularity of weak solutions to the Cahn–Hilliard equation with degenerate mobility. Moreover, we define a new entropy and obtain the global entropy estimates.

中文翻译：

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关于退化的Cahn–Hilliard方程：弱解的整体存在性和熵估计

在本文中，我们考虑了一类具有光滑双阱势的简并Cahn-Hilliard方程。通过对非退化的Cahn-Hilliard方程应用半离散化技术和渐近分析方法，我们获得了具有退化迁移率的Cahn-Hilliard方程的弱解的存在性和正则性。此外，我们定义了一个新的熵并获得了全局熵估计。