Abstract: We introduce a system modeling drug concentration and tumor growth associated with chemotherapy treatments for brain tumors, including different pharmacodynamics. It consists of a second order linear ODE and a non-linear parabolic PDE of Fisher-KPP type. First, we establish that the system is well-posed in an appropriate setting. Secondly, we study an associated optimal control problem, showing the existence of solution and deriving the first order necessary optimality conditions.

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