Qualitative Analysis Of Two Kinds Of Medical And Biological Mathematical Models

This thesis studies two kinds of medical and biological mathematical models.Firstly,a hyperbolic tumor model with necrotic nucleus is studied;the second is a simplified mathematical model based on the chronic wound healing of diabetes and obesity.These models are partial differential equation models derived from biology and medicine combined with biological principles and mathematical theory.The first problem is the necrotic hyperbolic tumor growth model with Robin free boundary.This model contains an elliptic equations describing the diffusion of nutrient,an ordinary differential equation describing tumor radius and three nonlinear first-order hyperbolic partial differential equation describing the evolution of proliferating cells,quiescent cells and dead cells,by applying the characteristic theory of hyperbolic equations and the Banach fixed point theorem,the existence and uniqueness of the global solutions of the model are proved.It is also proved that (?)R(t)=?in the case K_R=0.The second problem is the free boundary problem based on the chronic wound healing model of diabetes and obesity,this model contains the mutual coupling of the eleven parabolic equations,a hyperbolic equation and an elliptic equation.By using the relevant theory of parabolic equation and approximation method,the existence of weak solutions of the mathematical model are proved.The qualitative analysis of the above medical and biological mathematical models has not been studied.For the tumor growth model,the Dirichlet free boundary is mainly considered in the existing research,and we consider Robin free boundary by rigorous mathematical analysis in this thesis;For the wound healing model,the models of wound healing in diabetes or obesity are considered in the current study,this thesis mainly considers the well-posedness of the model of wound healing model in diabetes and obesity syndrome.