Optimal control of an Allen-Cahn model for tumor growth through supply of cytotoxic drugs. (English) Zbl 1514.92039
Summary: Our aim in this paper is to study an optimal control problem for a tumor growth model. The state system couples an Allen-Cahn equation and a reaction diffusion equation that models the evolution of tumor in the presence of nutrient supply. Elimination of cancer cells via cytotoxic drug is considered and the concentration of the cytotoxic drug is represented as a control variable.
MSC:
| 92C50 | Medical applications (general) |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35Q93 | PDEs in connection with control and optimization |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 49N90 | Applications of optimal control and differential games |
Keywords:
glioma treatment; Allen-Cahn equation; cytotoxic drugs; first order necessary optimality conditionsReferences:
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