We discuss the sharp interface limit of a diffuse interface model for a coupled Cahn-Hilliard--Darcy system that models tumor growth when a certain parameter $\varepsilon>0$, related to the interface thickness, tends to zero. In particular, we prove that weak solutions to the related initial boundary value problem tend to varifold solutions of a corresponding sharp interface model when $\varepsilon$ goes to zero.

中文翻译：

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用于肿瘤生长的扩散界面模型的锐界面极限的可变解

我们讨论了耦合 Cahn-Hilliard-Darcy 系统的扩散界面模型的尖锐界面限制，该系统在与界面厚度相关的某个参数 $\varepsilon>0$ 趋于零时对肿瘤生长进行建模。特别是，我们证明了当 $\varepsilon$ 变为零时，相关初始边值问题的弱解趋于对相应锐界面模型的变解。