Long term dynamics of the discrete growth-decay-fragmentation equation

TL;DR

This paper proves that for a broad class of growth-decay-fragmentation models, the solution semigroup exhibits analyticity and compactness, leading to the Asynchronous Exponential Growth property, which describes long-term behavior.

Contribution

It establishes the analyticity and compactness of the solution semigroup for a wide class of growth-decay-fragmentation equations, demonstrating their long-term exponential growth behavior.

Findings

Solution semigroup is analytic and compact

Models exhibit Asynchronous Exponential Growth

Long-term dynamics are characterized by exponential growth

Abstract

In this paper, we prove that for a large class of growth-decay-fragmentation problems the solution semigroup is analytic and compact and thus has the Asynchronous Exponential Growth property.