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一个肿瘤生长自由边界问题的研究 被引量：2

ON A FREE BOUNDARY PROBLEM MODELLING THE GROWTH OF TUMORS
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摘要 本文研究一个描述肿瘤生长的自由边界问题.这个自由边界问题是对Byrne和Chaplain相应肿瘤生长模型的一个改进,研究了该问题解当t→∞时的渐近状况,证明了未血管化的肿瘤体积不会无限制地增大,它或者趋于消失,或者趋于一个休眠态,依营养物浓度的大小和抑制物浓度的大小而定. This paper studies a free boundary problem modelling avascular tumor growth. This free boundary problem is an improvement of the tumor growth model proposed by Byrne and Chaplain. The authors study the asymptotic behavior of the solution, and prove that in the case where c1 and c2 are sufficiently small, the volume of an avascular tumor cannot expand unlimitedly, and it will either disappear or evolve to a dormant state as t→∞.
作者 冯兆永 崔尚斌
机构地区 中山大学数学系
出处 《数学年刊（A辑）》 CSCD 北大核心 2005年第3期403-412,共10页 Chinese Annals of Mathematics
基金 国家自然科学基金(No.10171112)资助的项目.
关键词 肿瘤生长 自由边界问题 局部解 整体解 渐近性态 Tumor growth, Free boundary problem, Local solution, Global solution, Asymptotic behavior
分类号 R730.2 [医药卫生—肿瘤]
  • 相关文献

参考文献15

  • 1Sutherland, R., Cell and environment interaction in tumor microregions: the multicell spheroid model [J], Science, 240(1988), 177-184.
  • 2Adam, J. & Bellomo, N., A Survey of Models for Tumor-immune System Dynamics[M], Birkhauser, Boston, 1997.
  • 3Greenspan, H., Models for the growth of solid tumors by diffusion [J], Stud. Appl.Math., 51(1972), 317-340.
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  • 5Ward, J. & King, J., Mathematical modelling of avascular tumor growth [J], IMA J.Math. Appl. in Biol. Med., 14(1997), 53-75.
  • 6Friedman, A. & Reitich, F., Analysis of a mathematical model for the growth of tumors [J], J. Math. Biol., 38(1999), 262-284.
  • 7Cui, S. & Friedman, A., Analysis of a mathematical model of the effect of inhibitors on the growth of tumors [J], Math. Biosci., 164(2000), 103-137.
  • 8Friedman, 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., 353(2000), 1587-1634.
  • 9Cui, S. & Friedman, A., Analysis of a mathematical model of the growth of necrotic tumors [J], J. Math. Anal. Appl., 255(2001), 636-677.
  • 10Cui, S., Analysis of a mathematical model for the growth of tumors under the action of external inhibitors [J], J. Math. Biol., 44(2002), 395-426.

二级参考文献11

  • 1Sutherland R. Cell and Environment Interactions in Tumor Microregions: the Multicell Spheroid Model. Science, 1988, 240:177-184
  • 2Adam J, Bellomo N. A Survey of Models for Tumor-immune System Dynamics. Boston: Birkhiuser, 1997
  • 3Greenspan H. Models for the Growth of Solid Tumors by Diffusion. Stud. Appl. Math., 1972, 51: 317-340
  • 4Adam J. A Simplified Mathematical Model of Tumor Growth. Math. Biosci., 1986, 81:224-229
  • 5Byrne H, Chaplain M. Growth of Nonnecrotic Tumors in the Presence and Absence of Inhibitors. Math. Biosci., 1995, 131:130-151
  • 6Ward J, King J. Mathematical Modeling of Avascular Tumor Growth Ⅱ: Modelling Growth Saturation. IMA J. Math. Appl. Med. Biol., 1998, 15:1-42
  • 7Pettet G, Please C, et al. The Migration of Cells in Multicell Tumor Spheroids. Bull. Math. Biol.,2001, 63:231-257
  • 8Friedman A, Reitich F. Analysis of a Mathematical Models for the Growth of Tumors. J. Math. Biol., 1999, 38:262-284
  • 9Cui S, Friedman A. Analysis of a Mathematical Model of the Effect of Inhibitors on the Growth of Tumors. Math. Biosci., 2000, 164:103-137
  • 10Cui S, Friedman A. Analysis of a Mathematical Model of the Growth of Necrotic Tumors. J. Math. Anal. Appl., 2001, 255:636-677

共引文献10

同被引文献10

  • 1卫雪梅,崔尚斌.一个肿瘤生长自由边界问题解的整体存在性和唯一性[J].数学物理学报（A辑）,2006,26(1):1-8. 被引量：10
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  • 5NEVILLE A A, MATTEWS P C, BYME H M. Interactions between pattern formation and domain Growth[J]. Bull Math Biol,2006,68:1 975-2 003.
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  • 7WARD J P, KING J R, Mathematical modeling of drug transport in tumor multicell spheroids and monolayer cultures [J]. Math Biol.2003,181: 177-207.
  • 8FRIEDMAN A, LOLAS G. Analysis of a mathematical model of tumor lymphangiogenesis[J]. Math Mod Math Appl Sci,2005,1: 95-107.
  • 9LADYZENSKAJA O A, SOLONNIKOV V A, URAL'CEVA N N. Linear and Quasi-Linear equations of parabolic type[J]. Amer Math Soc, 1968,23: 356-395.
  • 10闫欣荣.一类竞争扩散方程组的非平凡平衡态解[J].纺织高校基础科学学报,1998,11(2):167-170. 被引量：2

引证文献2

数学年刊（A辑）
2005年 第3期

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