A free boundary problem arising from branching Brownian motion with selection

Julien  Berestycki; Éric Brunet; James Nolen; Sarah Penington

doi:10.1090/tran/8370

A free boundary problem arising from branching Brownian motion with selection

Julien Berestycki, Éric Brunet, James Nolen, Sarah Penington

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Abstract

We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting particle system involving branching Brownian motion with selection, the so-called Brownian bees model which is studied in the companion paper (see Julien Berestycki, Éric Brunet, James Nolen, and Sarah Penington [Brownian bees in the infinite swarm limit, 2020]). In this paper we prove existence and uniqueness of the solution to the free boundary problem, and we characterise the behaviour of the solution in the large time limit.

Original language	English
Pages (from-to)	6269-6329
Number of pages	61
Journal	Transactions of the American Mathematical Society
Volume	374
Issue number	9
Early online date	18 May 2021
DOIs	https://doi.org/10.1090/tran/8370
Publication status	Published - 30 Sept 2021

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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A free boundary problem arising from branching Brownian motion with selection.pdf
First published in Transactions of the American Mathematical Society. vol 374 (2021), published by the American Mathematical Society. © 2021 American Mathematical Society.
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abstract = "We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting particle system involving branching Brownian motion with selection, the so-called Brownian bees model which is studied in the companion paper (see Julien Berestycki, {\'E}ric Brunet, James Nolen, and Sarah Penington [Brownian bees in the infinite swarm limit, 2020]). In this paper we prove existence and uniqueness of the solution to the free boundary problem, and we characterise the behaviour of the solution in the large time limit. ",

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AU - Nolen, James

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PY - 2021/9/30

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N2 - We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting particle system involving branching Brownian motion with selection, the so-called Brownian bees model which is studied in the companion paper (see Julien Berestycki, Éric Brunet, James Nolen, and Sarah Penington [Brownian bees in the infinite swarm limit, 2020]). In this paper we prove existence and uniqueness of the solution to the free boundary problem, and we characterise the behaviour of the solution in the large time limit.

AB - We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting particle system involving branching Brownian motion with selection, the so-called Brownian bees model which is studied in the companion paper (see Julien Berestycki, Éric Brunet, James Nolen, and Sarah Penington [Brownian bees in the infinite swarm limit, 2020]). In this paper we prove existence and uniqueness of the solution to the free boundary problem, and we characterise the behaviour of the solution in the large time limit.

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A free boundary problem arising from branching Brownian motion with selection

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