Qualitative Analysis Of A Class Of Nonlinear Tumor Growth Model

In this thesis,we study a necrotic nonlinear tumor growth model with Robin free boundary and a mathematical model of tumor spheroid experiments with real-time cell cycle imaging,these tumor growth mathematical models are both derived from the relevant research in biology and medicine.This thesis obtains the qualitative analysis of the corresponding problem by strict mathematical analysis.The first problem studied in this thesis is a nonlinear mathematical model of necrotic core tumor growth with Robin free boundary.By using the approximation method combines with the Lp-theory for parabolic equations and the Schauder fixed point theorem,and introducing a smooth function,this thesis proves the existence of the global weak solution of the model.The second problem studied in this thesis is a mathematical model of tumor spheroid experiments with real-time cell cycle imaging.The existence and uniqueness of the global classical solution of this model are obtained by applying the Lp-theory for parabolic equations,the characteristic line theory of hyperbolic equations and the Banach fixed point theorem.For the first mathematical model studied in this thesis,previous results consider the Dirichlet free boundary condition,we consider the Robin free boundary condition.It is a more meaningful free boundary condition.For the second mathematical model studied in this thesis,they have carried out numerical investigation,but the qualitative analysis of its solution has not been studied,this thesis analyses the qualitative analysis of its solution.