Analysis Of Two Mathematical Models Of Tumor Growth Effected By Immune Cells

In this paper, we study two models of tumor growth effected by immune cells, strictly analyzing the well-posedness of the solution: existence and uniqueness of the global solution for strongly coupled parabolic PDEs, and global existence for a free boundary problem. This paper consists of three chapters.In chapter 1, We make an introduction which involves background of the subject, current situation and significance of the subject, and relevant notions and preliminary lemmas.In chapter 2, a mathematical model of immune cells inhibiting tumor immune evasion is studied. The model involves strongly coupled parabolic PDEs. Applying the parabolic Lp-theory、Schauder-estimate and Banach Fixed Point Theorem, we prove that the problem has an unique local solution. Then by continuation method, we prove that the local solution is global.In chapter 3, we study a free boundary problem of breast tumor growth inhibited by macrophages. This problem is a mathematical model consisting of nine strongly coupled parabolic PDEs and an ODE. Firstly, this free boundary problem is transformed into an initial-boundary value problem in a fixed domain. Then, applying the parabolic Schauder-estimate theory, we prove that the free boundary problem exists global solution by using Schauder Fixed Point Theorem.