Garcke, Harald and Lam, Kei Fong and Rocca, Elisabetta (2018) Optimal Control of Treatment Time in a Diffuse Interface Model of Tumor Growth. APPLIED MATHEMATICS AND OPTIMIZATION, 78 (3). pp. 495-544. ISSN 0095-4616, 1432-0606
Full text not available from this repository. (Request a copy)Abstract
We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient and surrounded by host tissue. The introduction of cytotoxic drugs into the system serves to eliminate the tumor cells and in this setting the concentration of the cytotoxic drugs will act as the control variable. Furthermore, we allow the objective functional to depend on a free time variable, which represents the unknown treatment time to be optimized. As a result, we obtain first order necessary optimality conditions for both the cytotoxic concentration and the treatment time.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD SYSTEM; OPTIMAL DISTRIBUTED CONTROL; WELL-POSEDNESS; MIXTURE MODEL; DARCY SYSTEM; CHEMOTAXIS; EQUATION; Tumor growth; Cancer treatment; Free terminal time; Distributed optimal control; Cahn-Hilliard equation; Well-posedness |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 04 Oct 2019 09:39 |
| Last Modified: | 04 Oct 2019 09:39 |
| URI: | https://pred.uni-regensburg.de/id/eprint/13426 |
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