Differential and Integral Equations

On the stability of steady size-distributions for a cell-growth process with dispersion

Ronald Begg, Graeme C. Wake, and David J. N. Wall

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Abstract

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.

Article information

Source
Differential Integral Equations, Volume 21, Number 1-2 (2008), 1-24.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039056

Mathematical Reviews number (MathSciNet)
MR2479659

Zentralblatt MATH identifier
1224.92002

Subjects
Primary: 92C17: Cell movement (chemotaxis, etc.)
Secondary: 35B35: Stability 35Q92: PDEs in connection with biology and other natural sciences

Citation

Begg, Ronald; Wall, David J. N.; Wake, Graeme C. On the stability of steady size-distributions for a cell-growth process with dispersion. Differential Integral Equations 21 (2008), no. 1-2, 1--24. https://projecteuclid.org/euclid.die/1356039056


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