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非线性年龄依赖细胞分裂模型 被引量：2

Nonliear Age-Dependent Model of Cell Division
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摘要 讨论非线性年龄依赖带两阶段结构的细胞分裂模型,建立了增殖阶段和休眠阶段的年龄结构的等价模型,并证明了模型的解的存在唯一性. This paper analyses the nonliear age-dependent model of cell division with two-stage structure,the age-structure model with proliferating phase and resting pfase are established,and prove sxistence ang uniqueness of the solution.
作者 王定江
机构地区 浙江工业大学理学院
出处 《数学的实践与认识》 CSCD 北大核心 2007年第8期7-12,共6页 Mathematics in Practice and Theory
基金 国家自然科学基金(60543001) 浙江省自然科学基金(Y605075)
关键词 细胞模型 年龄结构 存在性 cell model age-structure existence
分类号 O221.3 [理学—运筹学与控制论]
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参考文献8

  • 1[1]Dyson J,Villella-Bressan R,Webb G F.A nonliear age and maturity structureed model of population dynamics.Ⅰ.Basic Theory[J].J Math Anal Appl,2000,242:93-104.
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同被引文献11

  • 1Farkas J Z, and Hinow P. On a size-structured two-phase population model with infinite states-at- birth[J]. Positivity, 2010, 14(3): 501-514.
  • 2Farkas J Z, Green D W, and Hinow P. Semigroup analysis of structured parasite populations[J]. Mathematical Modelling of Natural Phenomena, 2010(5): 94-114.
  • 3Auslander D M, Oster G F, and Huffaker C B. Dynamics of interacting populations[J]. J. Franklin Inst, 1974(297): 345-376.
  • 4Piazzera S, and Tonetto L. Asynchronous exponential growth for an age dependent population equation with delayed birth process[J]. J Evol Equ, 2005(5): 61-77.
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  • 6Dyson J, Villella-Bressan R, Webb G F. Asynchronous exponential growth in an age population of proliferating and quienscent cells[J]. Math Biosci, 2002, 177-178: 73-83.
  • 7Thieme H R. Balanced exponential growth of operator semigroups[J]. J Math Anal Appl 30-49. structured 1998(223).
  • 8Engel K J, and Nagel R. One-parameter Semigroups for Linear Evolution Equations[M]. Springer New York, 2000.
  • 9Ph. Clement H, Heijmans S, Angenent C, van Duijin and B. de Pagter. One-Parameter Semigroups[M]. North-holland, Amsterdam, 1987.
  • 10Arendt W, Grabosch A, Greiner G, Groh U, Lotz H P, Moustakas U, Nagel R, Neubrander F, and Schlotterbeck U. One-parameter Semigroups of Positive Operators[M]. Springer-Verlag, Berlin, North-holland, Amsterdam, 1987.

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数学的实践与认识
2007年 第8期

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