[1]徐剑磊,王泽佳,李景华.具抑制因子的肿瘤生长模型自由边界问题的分歧分析[J].江西师范大学学报(自然科学版),2016,40(02):204-208.
　XU Jianlei,WANG Zejia,LI Jinghua.The Bifurcation Analysis for a Free Boundary Problem Modeling Tumor Growth with Inhibitors[J].Journal of Jiangxi Normal University:Natural Science Edition,2016,40(02):204-208.
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具抑制因子的肿瘤生长模型自由边界问题的分歧分析()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
40
期数:
2016年02期
页码:
204-208
栏目:
出版日期:
2016-03-25

文章信息/Info

Title:
The Bifurcation Analysis for a Free Boundary Problem Modeling Tumor Growth with Inhibitors
作者:
徐剑磊;王泽佳;李景华
江西师范大学数学与信息科学学院,江西 南昌 330022
Author(s):
XU Jianlei; WANG Zejia; LI Jinghua
College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China
关键词:
自由边界问题;  稳态解;  分歧
Keywords:
free boundary problem;  stationary solution;  bifurcation
分类号:
O 175.26
文献标志码:
A
摘要:
研究具有抑制物因子的肿瘤生长模型的自由边界问题,主要分析该问题的分歧现象.此模型中肿瘤的进攻性由参数μ来描述,首先证明了该问题当半径r=Rs时有唯一径向对称稳态解.在此基础上还证明了存在正整数m∈R和序列μm,使得μm(m>m),均存在由径向对称稳态解分歧出来的非径向对称稳态解.
Abstract:
A free boundary problem modeling tumor growth with inhibitors is considered,and the bifurcation phenomenon of the problem is mainly analyzed.The aggressiveness is modeled by a positive tumor aggressiveness parameter μ.Firstly,it is proved that this problem has a unique radially symmetric stationary solution with radius r=Rs.On this basis,it is also shown that there exist a positive integer m∈R and a sequence of μm,such that for each μm(m>m),symmetric-breaking solutions bifurcate from the radially symmetric stationary solutions.

参考文献/References:

[1] Araujo R P,McElwain D L S.A history of the study of solid tumour growth:the contribution of mathematical modeling [J].Bull Math Biol,2004,66(5):1039-1091.
[2] Friedman A.A hierarchy of cancer models and their mathematical challenges [J].Discrete Contin Dyn Syst:Ser B,2004,4(1):147-159.
[3] Friedman A.Cancer models and their mathematical analysis [M].Berlin:Springer-Verlag,2006:223-246.
[4] Friedman A.Mathematical analysis and challenges arising from models of tumor growth [J].Math Models Methods Appl Sci,2007,17(1):1751-1772.
[5] Lowengrub J S,Frieboes H B,Jin Fang,et al.Nonlinear modelling of cancer:bridging the gap between cells and tumours [J].Nonlinearity,2010,23(1):1-9.
[6] Friedman A,Reitich F.Analysis of a mathematical model for the growth of tumors [J].J Math Biol,1999,38(3):262-284.
[7] Fontelos M A,Friedman A.Symmetry-breaking bifurcations of free boundary problems in three dimensions [J].Asymptot Anal,2003,35(3):187-206.
[8] Friedman A,Reitich F.Symmetry-breaking bifurcation of analytic solutions to free boundary problems:an application to a model of tumor growth [J].Trans Amer Math Soc,2001,353(4):1587-1634.
[9] Cui Shangbin.Analysis of a mathematical model for the growth of tumors under the action of external inhibitors [J].J Math Biol,2002,44(5):395-426.
[10] Cui Shangbin,Friedman A.Analysis of a mathematical model of the effect of inhibitors on the growth of tumors [J].Math Biosci,2000,164(2):103-137.
[11] Wang Zejia.Bifurcation for a free boundary problem modeling tumor growth with inhibitors [J].Nonlinear Anal RWA,2014,19(19):45-53.
[12] Friedman A,Hu Bei.Asymptotic stability for a free boundary problem arising in a tumor model [J].J Differential Equations,2006,227(2):598-639.
[13] Friedman A,Reitich F.Nonlinear stability of a quasi-static Stefan problem with surface tension:a continuation approach [J].Ann De Scuola Norm Sup Pisa Cl Sci,2000,30(4):341-403.
[14] Friedman A,Hu Bei.Stability and instability of Liapunov-Schmidt and Hopf bifurcation for a free boundary problem arising in a tumor model [J].Trans Amer Math Soc,2008,360(10):5291-5342.
[15] Crandall M G,Rabinowitz P H.Bifurcation from simple eigenvalues [J].J Functional Analysis,1971,8(2):321-340.

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备注/Memo

备注/Memo:
基金项目:国家自然科学基金(11361029),江西省自然科学基金(20142BAB211001)和江西省教育厅科学计划(GJJ14270)资助项目.
更新日期/Last Update: 1900-01-01