Ebenbeck, Matthias and Garcke, Harald and Nürnberg, Robert (2021) CAHN-HILLIARD-BRINKMAN SYSTEMS FOR TUMOUR GROWTH. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 14 (11). pp. 3989-4033. ISSN 1937-1632, 1937-1179
Full text not available from this repository. (Request a copy)Abstract
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FREE-BOUNDARY PROBLEM; PHASE FIELD MODEL; FINITE-ELEMENT APPROXIMATION; DARCY SYSTEM; NONLINEAR SIMULATION; MIXTURE MODEL; EQUATION; FORCHHEIMER; STABILITY; ALGORITHM; Cahn-Hilliard equation; phase field model; Brinkman model; existence; singular limit; finite elements; Tumour growth |
| Subjects: | 500 Science > 510 Mathematics 600 Technology > 610 Medical sciences Medicine |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Jul 2022 09:55 |
| Last Modified: | 05 Jul 2022 09:55 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46045 |
Actions (login required)
 |
View Item |
