A FREE BOUNDARY PROBLEM ARISING FROM BRANCHING BROWNIAN MOTION WITH SELECTION

被引：10
作者：
Berestycki, Julien [1 ]
Brunet, Eric
Nolen, James
Penington, Sarah
机构：
[1] Univ Oxford, Dept Stat, Oxford, England
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 374卷 / 09期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1090/tran/8370
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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, Eric 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.
引用
收藏
页码：6269 / 6329
页数：61
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