A free boundary problem with non local interaction

TL;DR

This paper proves local existence of classical solutions for a free boundary problem modeling biological selection, specifically the limit evolution of branching Brownian particles with leftmost particle death.

Contribution

It establishes local existence results for a free boundary problem linked to biological selection models, extending previous work on branching Brownian motion.

Findings

Proves local existence of classical solutions

Connects free boundary problems to biological selection models

Utilizes previous results to establish existence

Abstract

We prove local existence for classical solutions of a free boundary problem which arises in one of the biological selection models proposed by Brunet and Derrida, [2] and Durrett and Remenik, [14]. The problem we consider describes the limit evolution of branching brownian particles on the line with death of the leftmost particle at each creation time as studied in [12]. We use extensively results in [5] and [15].