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Analysis of cell population PDE models with general maturation rates

Published online by Cambridge University Press:  17 February 2009

Xinzhi Liu ,
S. Sivaloganathan  and
Shenghai Zhang
Xinzhi Liu
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada; e-mail: xzliu@monotone.uwaterloo.ca and ssivalog@sumathi.uwaterloo.ca.
S. Sivaloganathan
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada; e-mail: xzliu@monotone.uwaterloo.ca and ssivalog@sumathi.uwaterloo.ca.
Shenghai Zhang
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada; e-mail: shzhang@uwaterloo.ca.
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Abstract

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This paper considers a cell population model with a general maturation rate. This model is described by a nonlinear PDE. We use the theory of operator semigroups to stud the problem under simple hypotheses on the growth function and the nonlinear term. By showing that a related operator generates a strongly continuous semigroup, we prove the existence of a classical solution of the nonlinear problem and its positivity. It is also proved that under simple hypotheses, the problem generates a semiflow. The invariance of the semiflow is studied as well.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 3 , January 2002 , pp. 359 - 374
Copyright
Copyright © Australian Mathematical Society 2002

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