Existence And Uniqueness Of Global Solutions For Two Tumor Models

In this thesis, we study existence and uniqueness of global solutions to two tumor models. The thesis consists of four chapters.In Chapter 1, we first give an introduction to background and research significance of the study of tumor models, then we sketch main results of this paper.In Chapter 2, we introduce the relevant symbols and lemmas.In Chapter 3, we study a mathematical model of virotherapy in solid tumor in-vasion. The model is composed of four parabolic equations defined on fixed domain, one of which contains a cross-diffusion term. Firstly, we use Lp theory and Schauder estimate of parabolic equations and Banach fixed point theorem to prove existence and uniqueness of a local solution, then we use a priori estimates and extension method to prove global existence of this solution.In Chapter 4, we consider a mathematical model of GBM:effects of invasive cells and anti-angiogenesis. The model consists of a parabolic equation and four hyperbolic equations, with a free boundary being considered. Firstly, we convert the free boundary problem into an equivalent problem defined on fixed domain. Secondly, we use Lp theory of parabolic equations, characteristic theory of hyperbolic equations and Banach fixed point theorem to prove existence and uniqueness of a local solution. Finally we extend this local solution to be global by employing a priori estimate.