带有时滞项的肿瘤生长模型的数学分析

Analysis of mathematical models for the growthof tumors with time delays

本文研究三个带有时滞项的描述肿瘤生长的数学模型。时滞大小为细胞从开始分裂到新个体的形成所需要的时间。我们假设肿瘤生长没有抑制物作用,研究了问题解的存在唯一性及其初步性质和t→∞时解的渐近状态,证明了σ～<σ∞当时,未血管化的肿瘤体积不会无限制的增大或消失,且唯一存在的稳态解是一致渐近稳定的;当σ～≥σ∞时,未血管化的肿瘤体积不会无限制的增大,但有可能消失。

In this article, we study a mathematical model for the growth of tumors with time delays. The time delay represents the time taken for ceils to undergo mitosis. In the model, we assume that there is no inhibitor acting in the tumor. We study existence and uniqueness of solutions of this problem and the basic properties of its solutions. We also study the asymptotic behavior of the solution. We prove that when σ^-〈σ∞, the volume of the avascuiar tumor neither expand unlimitedly nor vanish, and the unique stationary solution is asymptotically stable. Whenσ^-〈σ∞, the volume of the avascular tumor cannot expand unlimitedly but probably can vanish.