CAHN-HILLIARD-BRINKMAN SYSTEMS FOR TUMOUR GROWTH

被引：16

作者：

Ebenbeck, Matthias ^{[1
]}

Garcke, Harald ^{[1
]}

Nurnberg, Robert ^{[2
]}

机构：

[1] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany

[2] Univ Trento, Dept Math, Trento, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2021年 / 14卷 / 11期

关键词：

Cahn-Hilliard equation; phase field model; Brinkman model; existence; singular limit; finite elements; Tumour growth; FREE-BOUNDARY PROBLEM; PHASE FIELD MODEL; FINITE-ELEMENT APPROXIMATION; DARCY SYSTEM; NONLINEAR SIMULATION; MIXTURE MODEL; EQUATION; FORCHHEIMER; STABILITY; ALGORITHM;

D O I：

10.3934/dcdss.2021034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A phase field model for tumour growth is introduced that is based on a Brinkman law for convective velocity fields. The model couples a con-vective 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.

引用

页码：3989 / 4033

页数：45

共 65 条

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