# American Institute of Mathematical Sciences

June  2019, 24(6): 2551-2576. doi: 10.3934/dcdsb.2018265

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

 CMAP-École Polytechnique, Route de Saclay, Palaiseau

* Corresponding author

Received  November 2017 Revised  April 2018 Published  October 2018

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.

Citation: Tristan Roget. On the long-time behaviour of age and trait structured population dynamics. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2551-2576. doi: 10.3934/dcdsb.2018265
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##### References:
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