论文标题
Cahn-Hilliard-Brinkman肿瘤生长系统
Cahn-Hilliard-Brinkman systems for tumour growth
论文作者
论文摘要
引入了肿瘤生长的相位场模型，该模型基于对流速度场的Brinkman定律。该模型将肿瘤的对流Cahn-Hilliard方程式融合到营养速度的营养和Brinkman-Stokes Type定律中，以使肿瘤的演变为反应扩散 - 添加方程。该模型是从基本的热力学原理得出的，尖锐的界面限制是由匹配的渐近学得出的，并且存在一个存在理论的迁移率的情况，该迁移率在一个相中退化，从而导致退化的抛物线方程式第四顺序。最后，数值结果描述了解决方案的定性特征，并在某些情况下说明了不稳定性。
A phase field model for tumour growth is introduced that is based on a Brinkman law for convective velocity fields. The model couples a convective Cahn-Hilliard equation for the evolution of the tumour to a reaction-diffusion-advection equation for a nutrient and to a Brinkman-Stokes type law for the fluid velocity. The model is derived from basic thermodynamical principles, sharp interface limits are derived by matched asymptotics and an existence theory is presented for the case of a mobility which degenerates in one phase leading to a degenerate parabolic equation of fourth order. Finally numerical results describe qualitative features of the solutions and illustrate instabilities in certain situations.
