On the stability of the cell size distribution

O. Diekmann, H. J.A.M. Heijmans, H. R. Thieme

Research output: Contribution to journalArticlepeer-review

159 Scopus citations


A model for the growth of a size-structured cell population reproducing by fission into two identical daughters is formulated and analysed. The model takes the form of a linear first order partial differential equation (balance law) in which one term has a transformed argument. Using semigroup theory and compactness arguments we establish the existence of a stable size distribution under a certain condition on the growth rate of the individuals. An example shows that one cannot dispense with this condition.

Original languageEnglish (US)
Pages (from-to)227-248
Number of pages22
JournalJournal Of Mathematical Biology
Issue number2
StatePublished - Apr 1984
Externally publishedYes


  • Balance equation
  • First-order partial differential equation
  • Reproduction by fission
  • Size-dependent population growth
  • Stable size distribution
  • Transformed arguments

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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