体外单层肿瘤细胞生长数学模型整体解的存在性

摘要

研究一个描述肿瘤生长的自由边界问题，它来源于Helen-Byrne描述的体外模拟单层肿瘤细胞连续性生长的数学模型。该模型主要研究肿瘤生长过程中细胞间的相互作用（张力和斥力）引起的内部变化。作者运用椭圆型偏微分方程的逼近方法、Lp理论和Schauder不动点理论证明了这个问题整体解的存在性。%A free boundary problem model of the growth of tumor which came from monolayer tumor cells model in vitro by Helen-Byrne was studied .With the model , internal change through cell-cell interactions was mainly studied using approximation method combined with Schauder fixed point theorem and the Lp-theory, it was proved that the problem had a global solution in any given time .