具抑制剂的血管化肿瘤生长模型的渐近分析

Asymptotic analysis of vascularized tumor growth model with inhibitor

研究具抑制剂的血管化肿瘤理论生长模型的偏微分方程自由边界问题,主要讨论解与自由边界的渐近行为。首先利用常微分方程理论得到了拟稳态解的存在唯一性;然后通过严格的分析,证明了在一定条件下limt→∞R(t)=0;最后运用迭代技巧,研究了解的渐近性态,得出在一定条件下,肿瘤模型的解将收敛于稳态解。

In this paper,we study a free boundary problem of partial differential equation modeling the growth model of vascularized tumor with inhibitors.Firstly,we show the existence and uniqueness of solution for the quasi-steady state problem by the theory of ordinary differential equation.Next,limt→∞R(t)=0 is obtained under some assumptions.Finally,the asymptotic behavior of the solution for the considered problem is discussed by the iterative technique.