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

数学物理学报 ›› 2010, Vol. 30 ›› Issue (2): 305-319.

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

吴俊德, 崔尚斌

中山大学数学与计算科学学院, 广州 |510275

收稿日期:2008-08-26 修回日期:2009-10-18 出版日期:2010-04-25 发布日期:2010-04-25
基金资助:
国家自然科学基金(10771223)资助.

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

WU Jun-De, CUI Shang-Bin

Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275

Received:2008-08-26 Revised:2009-10-18 Online:2010-04-25 Published:2010-04-25
Supported by:
国家自然科学基金(10771223)资助.

摘要/Abstract

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

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 for first-order partial differential equations, and the Banach fixed point theorem, existence and uniqueness of the global classic solution are established.

Key words: Tumor growth, Free boundary problem, Global solution

中图分类号:

34B15

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, 2010, 30(2): 305-319.

WU Jun-De, CUI Shang-Bin. 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,Series A, 2010, 30(2): 305-319.

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