The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution adapted to possible degeneracies and our main result is (global in time) existence. In order to overcome the lack of a-priori estimates, our proof uses the formal gradient flow structure of the system and an extension of the boundedness by entropy method which involves a careful analysis of an auxiliary variational problem. This allows to obtain solutions to an approximate, time-discrete system. Letting the time step size go to zero, we recover the desired weak solution where, due to their low regularity, the Cahn-Hilliard terms require a special treatment.

本文的目的是研究一种具有交叉扩散效应，简并迁移率且其中只有一个物种确实与另一个物种分离的多组分混合物的Cahn-Hilliard模型。我们定义了适用于可能的简并性的弱解的概念，我们的主要结果是（在时间上全局）存在。为了克服先验估计的不足，我们的证明使用系统的形式梯度流结构和通过熵方法扩展有界性，这涉及对辅助变分问题的仔细分析。这允许获得近似时间离散系统的解。让时间步长大小为零，我们恢复了所需的弱解，在这种情况下，由于其低规则性，Cahn-Hilliard项需要特殊处理。