A Free Boundary Problem Modeling The Growth Of Tumor Cord

With the continuous development of modern medicine, human beings gradually realizethat not all tumors are spherical. Spherical tumors include strictly spherical tumors and non-strictly spherical tumors, also include some other shapes of tumors such as the cylindricaltumors studied in this article. These tumors grow around the blood vessels, and the growthnutrients are provided by the blood vessels. The inner boundary of the tumor is fixed, whilethe outer boundary of the tumor is a free boundary. The domain outside of the free boundaryconsists of all necrosis tumor cells. Since such tumor is like a concentric cylinders, we call ittumor cord. On the mathematical model, this is a kind of problem composed of nonlineardiffusion equations, hyperbolic equations and the free boundary function. In order tounderstand the mechanism of tumor growth, we use rigorous mathematical analysis method tostudy the tumor model, and in this way we can provide strong mathematical support in theoryfor the tumors’ clinical medical research.This paper is devoted to the study of a free boundary problem modeling tumor tord.Rigorous mathematical analysis is given for the existence and uniqueness of global solutions.The contents of this paper are follows.In Chapter1, we respectively give an introduction to the background, the researchsignificance and the main result of this paper.In Chapter2, we introduce the required relevant symbols and lemmas.In Chapter3, we use a proper transformation to convert a free boundary problem into afixed boundary problem.In Chapter4, by using theLp theory and the Schauder estimates of parabolic equationand the Banach fixed point theorem, we prove that this system has a unique local solution.In Chapter5, we ultilize the extension theory to prove that solutions of the originalproblem are global.