Garcke, Harald and Lam, Kei Fong (2017) Well-posedness of a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 28 (2). pp. 284-316. ISSN 0956-7925, 1469-4425
Full text not available from this repository. (Request a copy)Abstract
We consider a diffuse interface model for tumour growth consisting of a Cahn-Hilliard equation with source terms coupled to a reaction-diffusion equation. The coupled system of partial differential equations models a tumour growing in the presence of a nutrient species and surrounded by healthy tissue. The model also takes into account transport mechanisms such as chemotaxis and active transport. We establish well-posedness results for the tumour model and a variant with a quasi-static nutrient. It will turn out that the presence of the source terms in the Cahn-Hilliard equation leads to new difficulties when one aims to derive a priori estimates. However, we are able to prove continuous dependence on initial and boundary data for the chemical potential and for the order parameter in strong norms.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIFFUSE INTERFACE MODEL; LONG-TIME BEHAVIOR; HELE-SHAW CELL; MIXTURE MODEL; RECONNECTION; SIMULATION; PINCHOFF; Tumour growth; phase field model; Cahn-Hilliard equation; reaction-diffusion equations; chemotaxis; weak solutions; well-posedness |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:11 |
| Last Modified: | 25 Feb 2019 18:43 |
| URI: | https://pred.uni-regensburg.de/id/eprint/1159 |
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