Asynchronous exponential growth for structured population models in measure space
Abstract
This paper studies the asymptotic behaviour of a structured population model on the space of nonnegative Radon measures. Such formulations naturally arise when solutions develop concentration phenomena or when the population is represented by discrete cohorts. Asynchronous exponential convergence of measure solutions towards a one-dimensional global attractor is established. While such results are classical in the setting, their extension to measure spaces requires different compactness and spectral arguments. We identify conditions under which the classical asymptotic behaviour persists in the space of Radon measures endowed with the flat metric, thereby extending the theory of asynchronous exponential growth beyond the classical framework.
Cite
@article{arxiv.2607.00658,
title = {Asynchronous exponential growth for structured population models in measure space},
author = {Christian Düll and József Z. Farkas and Piotr Gwiazda and Anna Marciniak-Czochra},
journal= {arXiv preprint arXiv:2607.00658},
year = {2026}
}