# Existence of the global solutions of an integro-differential equation in population dynamics

## TL;DR

This paper proves that a nonlinear integro-differential equation in population dynamics has solutions that exist for all time, extending previous local existence results to global solutions through a priori estimates.

## Contribution

The paper establishes the global existence of solutions for a specific nonlinear integro-differential equation in population dynamics, building on prior local existence results.

## Key findings

- Solutions are globally existing in time
- A priori estimates are derived to extend local solutions
- The dynamics remain well-defined for all time

## Abstract

We study a nonlinear integro-differential equation arising in population dynamics. It has been already proved by Rybka, Tang and Waxman that it has a unique local in time solution. Here, after deriving appropriate a priori estimates we show that the dynamics is global in time.