# Self-similar solutions of fragmentation equations revisited

## TL;DR

This paper investigates the long-term behavior of particle sizes in fragmentation processes, establishing conditions under which solutions converge to a unique self-similar form, enhancing understanding of particle size distribution evolution.

## Contribution

It provides necessary and sufficient conditions for the convergence of solutions to the self-similar solution in fragmentation equations with homogeneous kernels.

## Key findings

- Identifies conditions for convergence to self-similarity
- Characterizes the large-time behavior of particle size distributions
- Ensures uniqueness of the self-similar solution

## Abstract

We study the large time behaviour of the mass (size) of particles described by the fragmentation equation with homogeneous breakup kernel. We give necessary and sufficient conditions for the convergence of solutions to the unique self-similar solution.