Garcke, Harald and Lam, Kei Fong and Signori, Andrea (2021) On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 57: 103192. ISSN 1468-1218,
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Mechanical effects have mostly been neglected so far in phase field tumour models that are based on a Cahn-Hilliard approach. In this paper we study a macroscopic mechanical model for tumour growth in which cell-cell adhesion effects are taken into account with the help of a Ginzburg-Landau type energy. In the overall model an equation of Cahn-Hilliard type is coupled to the system of linear elasticity and a reaction-diffusion equation for a nutrient concentration. The highly nonlinear coupling between a fourth-order Cahn-Hilliard equation and the quasi-static elasticity system lead to new challenges which cannot be dealt within a gradient flow setting which was the method of choice for other elastic Cahn-Hilliard systems. We show existence, uniqueness and regularity results. In addition, several continuous dependence results with respect to different topologies are shown. Some of these results give uniqueness for weak solutions and other results will be helpful for optimal control problems. (C) 2020 Elsevier Ltd. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIFFUSE INTERFACE MODEL; NUMERICAL-SIMULATION; GINZBURG-LANDAU; MIXTURE MODEL; SOLID STRESS; DARCY MODEL; SEPARATION; APPROXIMATION; CHEMOTAXIS; VALIDATION; Tumour growth; Cahn-Hilliard equation; Mechanical effects; Linear elasticity; Elliptic-parabolic system; Existence and uniqueness |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 13 Sep 2022 06:41 |
| Last Modified: | 13 Sep 2022 06:41 |
| URI: | https://pred.uni-regensburg.de/id/eprint/47252 |
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