Abstract
An optimal control problem for a general reaction-diffusion tumor-immune interaction system under immunotherapy and chemotherapy is discussed to minimize the weighted tumor burden, side effects and treatment costs. The existence, uniqueness and some estimates of strong solution to the state system are obtained by means of the truncation method and semigroup theory. We verify the existence of optimal pair by utilizing the technique of minimizing sequence. The first-order necessary optimality condition and characterization of the optimal control are also derived by proving the differentiability of the control-to-state mapping. In addition, some numerical simulations for this optimal control problem are carried out to present the numerical verification and concrete realization of the theoretical results obtained in this work.
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