# Mass-conserving self-similar solutions to coagulation-fragmentation equations

## TL;DR

This paper proves the existence of mass-conserving self-similar solutions for certain coagulation-fragmentation equations with small total mass, using a dynamical and compactness approach.

## Contribution

It introduces a novel method combining dynamical systems and compactness techniques to establish solutions for a class of coagulation-fragmentation equations.

## Key findings

- Existence of solutions for small total mass
- Mass conservation in self-similar solutions
- Application of dynamical and compactness methods

## Abstract

Existence of mass-conserving self-similar solutions with a sufficiently small total mass is proved for a specific class of homogeneous coagulation and fragmentation coefficients. The proof combines a dynamical approach to construct such solutions for a regularised coagulation-fragmentation equation in scaling variables and a compactness method.