On the long-time behaviour of age and trait structured population dynamics

Tristan Roget

doi:10.3934/dcdsb.2018265

Article Contents

2019, Volume 24, Issue 6: 2551-2576. Doi: 10.3934/dcdsb.2018265

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On the long-time behaviour of age and trait structured population dynamics

Tristan Roget^,

CMAP-École Polytechnique, Route de Saclay, Palaiseau

* Corresponding author
* Corresponding author

Received: October 31, 2017

Revised: March 31, 2018

Early access: October 2018

Published: June 2019

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Abstract

We study the long-time behaviour of a population structured by age and a phenotypic trait under a selection-mutation dynamics. By analysing spectral properties of a family of positive operators on measure spaces, we show the existence of eventually singular stationary solutions. When the stationary measures are absolutely continuous with a continuous density, we show the convergence of the dynamics to the unique equilibrium.

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Mathematics Subject Classification: Primary: 35B40, 92D25; Secondary: 35P05, 60J80.

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