Ebenbeck, Matthias and Knopf, Patrik (2019) Optimal medication for tumors modeled by a Cahn-Hilliard-Brinkman equation. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 58 (4): 131. ISSN 0944-2669, 1432-0835
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In this paper, we study a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn-Hilliard type equation for the phase field variable coupled to a reaction diffusion equation for the nutrient and a Brinkman type equation for the velocity. The system is equipped with homogeneous Neumann boundary conditions for the tumor variable and the chemical potential, Robin boundary conditions for the nutrient and a no-friction boundary condition for the velocity. The control acts as a medication by cytotoxic drugs and enters the phase field equation. The cost functional is of standard tracking type and is designed to track the variables of the state equation during the evolution and the distribution of tumor cells at some fixed final time. We prove that the model satisfies the basics for calculus of variations and we establish first-order necessary optimality conditions for the optimal control problem.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIFFUSE INTERFACE MODEL; WELL-POSEDNESS; DARCY SYSTEM; GROWTH; CHEMOTAXIS; SIMULATION; TIME; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke Mathematics > Prof. Dr. Guido Kings |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Apr 2020 06:18 |
| Last Modified: | 07 Apr 2020 06:18 |
| URI: | https://pred.uni-regensburg.de/id/eprint/26560 |
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