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On the stability of steady size-distributions for a cell-growth process with dispersion. (English) Zbl 1224.92002
Summary: The model discussed in this paper describes the evolution of the size-distribution of a population of cells in time. It is assumed that there is a degree of stochasticity in the growth process of each individual cell in the population. This manifests itself as a dispersion term in the differential equation for the evolution of the size-distribution of the overall population. We study the stability of the steady size-distributions (SSDs) of the model (the spatial components of separable solutions) and show that given a set of parameters, where an SSD exists, it is unique and globally asymptotically stable.

92C37 Cell biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35B35 Stability in context of PDEs