One-sided FKPP travelling waves in the context of homogeneous fragmentation processes

TL;DR

This paper introduces a new one-sided FKPP equation tailored for homogeneous fragmentation processes, establishing existence, uniqueness, and analytic properties of its travelling wave solutions using advanced probabilistic techniques.

Contribution

It is the first to analyze one-sided FKPP travelling waves in the context of homogeneous fragmentation processes, providing foundational results and methods.

Findings

Existence of one-sided FKPP travelling waves

Uniqueness of these travelling waves

Analytic properties of the solutions

Abstract

In this paper we introduce the one-sided FKPP equation in the context of homogeneous fragmentation processes. The main result of the present paper is concerned with the existence and uniqueness of one-sided FKPP travelling waves in this setting. Moreover, we prove some analytic properties of such travelling waves. Our techniques make use of fragmentation processes with killing, an associated product martingale as well as various properties of L\'evy processes.