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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.

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