Modélisation de la chimiotaxie tumorale et Équations aux Dérivées partielles

Abstract

This thesis studies chemotaxis, a directed cell migration driven by a chemical gradient, through Keller-Segel models and their modern variants. Chapter 2 presents the mathematical modeling framework, the different types of taxis, and the application to tumor and immune interactions. Chapter 3 focuses on the global existence of very weak solutions for a chemotaxis system with a logistic source. Following Winkler's strategy, a priori estimates are derived and the limit passage is achieved by compactness arguments. The study shows that consumption effects and boundary conditions can prevent blow-up.