A short remark on a Growth Fragmentation equation

TL;DR

This paper derives an explicit local solution for a growth fragmentation equation with constant dislocation measure, demonstrating finite-time blow-up and highlighting limitations of existing global solution criteria.

Contribution

It provides a specific explicit solution for a growth fragmentation equation where standard global existence conditions fail, illustrating finite-time blow-up.

Findings

Explicit local solution obtained

Solution blows up in finite time

Highlights limitations of previous global existence results

Abstract

An explicit solution for a growth fragmentation equation with constant dislocation measure is obtained. In this example the necessary condition for the general results in \cite{BW} about the existence of global solutions in the so called self similar case is not satisfied. The solution is local and blows up in finite time.