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.
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Diekmann, O., Heijmans, H.J.A.M. & Thieme, H.R. On the stability of the cell size distribution. J. Math. Biology 19, 227–248 (1984). https://doi.org/10.1007/BF00277748
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DOI: https://doi.org/10.1007/BF00277748