Tumor growth model with chemotaxis and active transport: Control and parameters recovery

In this paper, we formulate and analyze an optimal control problem for a system of Cahn–Hilliard equations modeling tumor growth, accounting for chemotaxis and active transport. The dynamical system was introduced in Hawkins-Daarud et al. (2012), and mathematical results of existence and uniqueness of weak solutions were obtained in Garcke and Yayla (2020). In this contribution, we prove the continuous dependence of the solutions on the physical parameters in addition to the initial data. In addition, we introduce an optimal control problem where the cost functional depends on a target function, but most importantly, on physical parameters targets. We establish the existence of a unique minimizer and provide optimality conditions. Eventually, we present simple numerical illustrations in full agreement with our theoretical results.