On a size-structured two-phase population model with infinite states-at-birth

Details On a size-structured two-phase population model with infinite states-at-birth On a size-structured two-phase population model with infinite states-at-birth

2009-03-09

arxiv.org/abs/0903.1649v2

Positivity 14 (2010), 501-514

Mathematics

Analysis of PDEs

1 figure, to appear in Positivity

Scientific paper

10.1007/s11117-009-0033-4

In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an "active" phase when individuals grow, reproduce and die and a second "resting" phase when individuals only grow. Transition between these two phases depends on individuals' size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.

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