Details

Autor(en) / Beteiligte

• Farkas, József Z.
• Hinow, Peter

Titel

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

Ist Teil von

• Positivity : an international journal devoted to the theory and applications of positivity in analysis, 2010-09, Vol.14 (3), p.501-514

Ort / Verlag

Basel: SP Birkhäuser Verlag Basel

Erscheinungsjahr

2010

Link zum Volltext

Quelle

Business Source Ultimate

Beschreibungen/Notizen

• 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.