Some Remarks About the Semigroup Associated to Age-Structured Diffusive Populations

TL;DR

This paper analyzes the mathematical properties of age-structured population models with diffusion, focusing on the generator and spectral characteristics of the associated semigroup to understand stability and growth behaviors.

Contribution

It characterizes the generator and spectral properties of the semigroup for age-structured diffusive populations under maximal regularity assumptions.

Findings

Conditions for stability of the zero solution

Criteria for asynchronous exponential growth

Spectral properties of the associated semigroup

Abstract

We consider linear age-structured population equations with diffusion. Supposing maximal regularity of the diffusion operator, we characterize the generator and its spectral properties of the associated strongly continuous semigroup. In particular, we provide conditions for stability of the zero solution and for asynchronous exponential growth.