一个药物作用肿瘤生长自由边界问题整体解的存在唯一性  

Existence and Uniqueness of Global Solutions for a Free Boundary Problem Modeling the Growth of Tumors under the Action of Drugs

作　　者：吴俊德[1] 崔尚斌[1] 

机构地区：[1]中山大学数学与计算科学学院,广州510275

出　　处：《数学物理学报（A辑）》2010年第2期305-319,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(10771223)资助

摘　　要：该文研究一个描述药物作用下肿瘤生长的数学模型,这个肿瘤模型是对Jackson模型的一个改进,其数学形式是由一个二阶非线性抛物型方程与两个一阶非线性偏微分方程组耦合而成的自由边界问题.通过运用抛物型方程的L^P理论与一阶偏微分方程的特征方法,并利用Banach不动点定理,证明了该问题存在唯一的整体经典解.In this paper a mathematical model for the effect of drugs in the growth of tumors is studied.This model is a modification of the Jackson model by dividing tumor cells into three classes：proliferating cells,dormant cells and dead cells.The model is a free boundary problem of a system of partial differential equations comprising a second-order nonlinear parabolic equation and two first-order nonlinear partial differential equations.By applying the L^p theory of parabolic equations,the characteristic method for first-order partial differential equations, and the Banach fixed point theorem,existence and uniqueness of the global classic solution are established.

关 键 词：肿瘤生长 自由边界问题 整体解 

分 类 号：O175.2[理学—数学]