Analysis of a Radiotherapy Model for Brain Tumors

TL;DR

This paper investigates a mathematical model for brain tumors influenced by radiotherapy, proving existence, uniqueness, and regularity of solutions, and analyzing optimal control of radiotherapy effects with numerical validation.

Contribution

It provides new analytical results on the existence, uniqueness, and regularity of solutions, and explores optimal control strategies in a radiotherapy tumor model.

Findings

Proved existence and uniqueness of solutions under certain conditions

Established additional regularity for solutions with regular initial data

Numerical illustrations support analytical results

Abstract

In this work, we focus on the analytical and numerical study of a mathematical model for brain tumors with radiotherapy influence. Under certain assumptions on the given data in the model, we prove existence and uniqueness of a weak nonnegative (biological relevant) solution. Then, assuming only more regular initial data, we obtain the extra regularity of this solution. Besides, we analyze the optimal control of the advection coefficient responding for the radiotherapy effect on the tumor cell population. Finally, we provide numerical illustration to all obtained analytical results.