具有趋化性的Cahn-Hilliard-Brinkman肿瘤生长模型分析
Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis
摘要：
相场模型最近在肿瘤生长模型的背景下获得了很大的兴趣。典型的Darcy型流动模型与Cahn-Hilliard方程耦合。然而，斯托克斯或布林克曼流动通常是更合适的流动模型。我们介绍和数学分析一个新的Cahn-Hilliard-Brinkman模型允许肿瘤生长的趋化性。考虑了流出边界条件，以避免人工边界条件对肿瘤生长的影响。在一个非常一般的设置下，显示了整体的时间弱解的存在性。
英文摘要：
Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn-Hilliard equations. However, often Stokes or Brinkman flows are more appropriate flow models. We introduce and mathematically analyse a new Cahn-Hilliard-Brinkman model for tumour growth allowing for chemotaxis. Outflow boundary conditions are considered in order not to influence tumour growth by artificial boundary conditions. Existence of global-in-time weak solutions is shown in a very general setting.
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