Hilhorst, Danielle and Kampmann, Johannes and Thanh Nam Nguyen, and Van Der Zee, Kristoffer George (2015) Formal asymptotic limit of a diffuse-interface tumor-growth model. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 25 (6). ISSN 0218-2025, 1793-6314
Full text not available from this repository. (Request a copy)Abstract
We consider a diffuse-interface tumor-growth model which has the form of a phase-field system. We characterize the singular limit of this problem. More precisely, we formally prove that as the coefficient of the reaction term tends to infinity, the solution converges to the solution of a novel free boundary problem. We present numerical simulations which illustrate the convergence of the diffuse-interface model to the identified sharp-interface limit.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD EQUATION; PHASE FIELD MODEL; SINGULAR LIMIT; SIMULATION; CONVERGENCE; BOUNDARY; Reaction-diffusion system; singular perturbation; interface motion; matched asymptotic expansion; tumor-growth model; phase-field model; gradient flow; stabilized Crank-Nicolson method; convex-splitting scheme |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 10 Jul 2019 14:12 |
| Last Modified: | 10 Jul 2019 14:12 |
| URI: | https://pred.uni-regensburg.de/id/eprint/5319 |
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