Optimal control for a free boundary tumor growth model

Abstract

This paper investigates the optimal control of treatment in a free boundary PDE model that describes the growth of a radially symmetric tumor. The optimal control strategy is designed to inhibit tumor growth while minimizing side effects. We establish the well-posedness of the problem and prove the existence of an optimal control. In order to characterize this optimal control, the optimality system is derived, and a necessary condition is obtained. Numerical simulations are conducted to illustrate our theoretical findings and assess the impact of the optimal control strategy on tumor growth dynamics. Furthermore, we extend the model to include spatial dependency in the control variable and perform additional simulations to explore this more complex scenario.