Theoretical analysis for a PDE-ODE system related to a Glioblastoma tumor with vasculature

TL;DR

This paper provides a rigorous mathematical analysis of a PDE-ODE system modeling Glioblastoma with vasculature, establishing existence, uniqueness, and stability of solutions to better understand tumor dynamics.

Contribution

It introduces a simplified PDE-ODE model for Glioblastoma and proves key mathematical properties, including global existence, uniqueness, and stability of solutions.

Findings

Existence and uniqueness of global classical solutions

Stability results depending on parameter conditions

Mathematical framework for tumor-vasculature modeling

Abstract

In this paper we study a PDE-ODE system as a simplification of a Glioblastoma model. Mainly, we prove the existence and uniqueness of global in time classical solution using a fixed point argument. Moreover, we show some stability results of the solution depending on some conditions on the parameters.