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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
引用本文:吴俊德,崔尚斌.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[J].数学物理学报(A辑),2010,30(2):305-319.
作者姓名:吴俊德  崔尚斌
作者单位:中山大学教学与计算科学学院,广州,510275 
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.

关 键 词:肿瘤生长  自由边界问题  整体解
收稿时间:2008-08-26
修稿时间:2009-10-18

Existence and Uniqueness of Global Solutions for a Free Boundary Problem Modeling the Growth of Tumors under the Action of Drugs
Wu Junde Cui Shangbin.Existence and Uniqueness of Global Solutions for a Free Boundary Problem Modeling the Growth of Tumors under the Action of Drugs[J].Acta Mathematica Scientia,2010,30(2):305-319.
Authors:Wu Junde Cui Shangbin
Institution:Wu Junde Cui Shangbin (Department of Mathematics,Sun Yat-Sen University,Guangzhou 510275)
Abstract: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 f...
Keywords:Tumor growth  Free boundary problem  Global solution
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