A free boundary problem in biological selection models

TL;DR

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

Contribution

It establishes the local existence of solutions for a biologically motivated free boundary problem, extending previous work on particle systems and free boundary analysis.

Findings

Proved local existence of classical solutions.

Connected free boundary problems with biological selection models.

Utilized existing mathematical results to establish solution properties.

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, [3]. 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 [7]. We use extensively results in [1] and [2].