# Mass-conserving solutions to coagulation-fragmentation equations with balanced growth

## TL;DR

This paper studies a special class of coagulation-fragmentation equations where coagulation and fragmentation are balanced, proving existence and uniqueness of mass-conserving solutions for small initial mass.

## Contribution

It introduces a specific class of coefficients ensuring mass conservation and establishes existence and uniqueness results under small initial mass conditions.

## Key findings

- Existence of mass-conserving solutions for small initial mass
- Uniqueness of solutions in the considered class
- Balance between coagulation and fragmentation coefficients

## Abstract

A specific class of coagulation and fragmentation coefficients is considered for which the strength of the coagulation is balanced by that of the multiple fragmentation. Existence and uniqueness of mass-conserving solutions are proved when the initial total mass is sufficiently small.