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一个带有时滞项的肿瘤生长模型解的存在唯一性

Existence and Uniqueness of Solution of a Mathematical Model for tumor growth with time delays
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摘要 研究了一个带有时滞项的描述肿瘤生长的数学模型解的存在唯一性,时滞大小为细胞从开始分裂到新个体的形成所需要的时间. We study existence and uniqueness of a mathematical model for the growth of tumors with time delays. The time delay represents the time taken for cells to undergo mitosis.
作者 徐士河
机构地区 肇庆学院数学系
出处 《喀什师范学院学报》 2007年第3期22-23,共2页 Journal of Kashgar Teachers College
基金 肇庆学院青年基金项目(0635)
关键词 肿瘤生长 时滞微分方程 整体解 Tumor growth Retarded differential equation Global solution
分类号 O177.92 [理学—基础数学]
  • 相关文献

参考文献5

  • 1Friedman A,Reitich F.Analysis of a Mathematical Model for the Growth of Tumors[J].J Math Bio1,1999,38:262-284.
  • 2郑祖麻.泛函微分方程理论[J].安徽教育出版社,1994.
  • 3Cui S.Analysis of a Mathematical Model for the Growth of Tumors under the Action of External Inhibitors[J].J Math Biol,2002,44:395-426.
  • 4崔尚斌,艾军.关于抑制物对肿瘤生长直接效果模型的数学分析[J].应用数学学报,2002,25(4):617-625. 被引量：11
  • 5Cui S,Friedman A.Analysis of a Mathematical Model of the Effect of Inhibitors on the Growth of Tumors[J].Math Biosci,2000,164:103-137.

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

喀什师范学院学报
2007年 第3期

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