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  • 1
    Electronic Resource
    Electronic Resource
    On the stability of the cell size distribution (1984)
    Springer
    Journal of mathematical biology 19 (1984), S. 227-248 
    Details
    ISSN: 1432-1416
    Keywords: Size-dependent population growth ; Reproduction by fission ; Balance equation ; First-order partial differential equation ; Transformed arguments ; Stable size distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00277748
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  • 2
    Electronic Resource
    Electronic Resource
    Growth, fission and the stable size distribution (1983)
    Springer
    Journal of mathematical biology 18 (1983), S. 135-148 
    Details
    ISSN: 1432-1416
    Keywords: Size-dependent population growth ; Reproduction by fission ; Balance equation ; First order p.d.e. ; Transformed arguments ; nutrient limitation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model for the growth of a size-structured population reproducing by fission and living under changing (nutrient) conditions is formulated and analysed. It is shown that the dynamics is asymptotically described by an o.d.e. total population model, while the size distribution becomes stationary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00280662
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