Analysis of a Radiotherapy Model for Brain Tumors

In this work, we focus on the analytical and numerical study of a mathematical model for brain tumors undergoing radiotherapy treatment. Under certain assumptions regarding the given data in the model, we prove the existence and uniqueness of a weak nonnegative (biologically relevant) solution. Then, we show how the additional regularity of initial data affects the regularity of these solutions. Besides, we analyze the optimal control of the advection coefficient which tunes the radiotherapy effect on the tumor cell population. We also complement our analytical results with relevant numerical simulations.