Asymptotic Analysis Of Solutions For Vascularized Tumor Model With Time Delay

In this thesis,we study the free boundary problem of spherical vascularized tumor growth model with time delay.We analyze the vascularized tumor growth model with time delay in the process of regulating apoptosis,the vascularized tumor growth model with inhibitors and time delay respectively.We discuss the existence,uniqueness and stability of the steady-state solution,the asymptotic behavior of tumor radius R(t),and the main results of this paper are verified by numerical simulation.This thesis is divided into three chapters.In chapter 1,we mainly introduce the known research related on the free boundary problem of tumor growth model,also state our main results and preliminaries.In chapter 2,we study the free boundary problem of vascularized tumor growth model with time delay.The parameters σ∞,σ,σh,θ denote the nutrient concentration outside the tumor,nutrient concentration threshold of cell mitosis and the optimal growth rate of the tumor respectively,we analyze the existence,uniqueness and stability of the steady-state solution,the global existence,uniqueness and asymptotic behavior of the time-varying solution in quasi-steady state and completely unsteady state under the assumption that σh>σ>σ∞.We prove that if(σ-σ∞)/(σh-σ∞)<θ<σ/σh,the positive steady-state solution is unique and stable.The results show that due to the existence of the regulating apoptosis,the positive steady-state solution exists and is stable even if the deficiency of nutrient,which is different from those for tumor model without the regulating apoptosis.In chapter 3,we study the free boundary problem of vascularized tumor growth with inhibitors and time delay,we first establish the existence and uniqueness of the non-negative solution to this problem,and then give the relationship between the vascularization degree function α(t)and tumor radius R(t).It is proved that R(t)is also bounded when α(t)is bounded,and when α(t)is an almost periodic function,there is an unique almost periodic solution to this problem.