Asymptotic behaviour of a structured population model on a space of measures

TL;DR

This paper analyzes a structured population model on measures, demonstrating how semigroup theory ensures solutions converge exponentially to a global attractor, revealing long-term population behavior.

Contribution

It introduces a framework applying semigroup theory to measure-based population models, establishing exponential convergence to equilibrium.

Findings

Solutions converge exponentially to a one-dimensional attractor

The model is formulated on the space of Radon measures

The approach uses the pre-dual space of bounded Lipschitz functions

Abstract

In this paper we consider a physiologically structured population model with distributed states at birth, formulated on the space of non-negative Radon measures. Using a characterisation of the pre-dual space of bounded Lipschitz functions, we show how to apply the theory of strongly continuous positive semigroups to such a model. In particular, we establish the exponential convergence of solutions to a one-dimensional global attractor.