论文标题
退化Cahn-Hilliard方程：从非本地到本地
Degenerate Cahn-Hilliard equation: From nonlocal to local
论文作者
论文摘要
最近，对从非局部方程的严格得出Cahn-Hilliard方程的严格兴趣，也称为聚合方程。到目前为止，仅处理非分类的迁移率。由于我们是由生物组织生物力学模型激发的，因此包括退化运动能力很有用。在此框架中，我们提出了一种新方法，以显示非局部与局部退化Cahn-Hilliard方程的收敛性。该方法包括使用非局部庞加莱和紧凑性不等式。
There has been recently an important interest in deriving rigorously the Cahn-Hilliard equation from the nonlocal equation, also called aggregation equation. So far, only non-degenerate mobilities were treated. Since we are motivated by models for the biomechanics of living tissues, it is useful to include degenerate motilities. In this framework, we present a new method to show the convergence of the nonlocal to the local degenerate Cahn-Hilliard equation. The method includes the use of nonlocal Poincaré and compactness inequalities.
