论文标题
存在跨扩散Cahn-Hilliard类型系统的薄弱解决方案
Existence of weak solutions to a cross-diffusion Cahn-Hilliard type system
论文作者
论文摘要
本文的目的是研究具有交叉扩散效果，退化迁移率的多组分混合物的Cahn-Hilliard模型，其中只有一个物种确实与其他物种分开。我们定义了一个适合可能的变性的弱解决方案的概念，我们的主要结果是（全球）存在。为了克服缺乏A-Priori估计值，我们的证明使用系统的形式梯度流结构，并通过熵方法扩展了界限，该方法涉及对辅助变异问题的仔细分析。这允许获取近似时间二散系统的解决方案。让时间步长达到零，我们恢复了所需的弱解决方案，由于其规律性低，Cahn-Hilliard术语需要特殊处理。
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.
