A free boundary problem arising from branching Brownian motion with selection

Julien Berestycki, Éric Brunet, James Nolen, Sarah Penington

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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 languageEnglish
Pages (from-to)6269-6329
Number of pages61
JournalTransactions of the American Mathematical Society
Issue number9
Early online date18 May 2021
Publication statusPublished - 30 Sept 2021

Bibliographical note

Funding Information:
Received by the editors June 23, 2020, and, in revised form, November 17, 2020. 2020 Mathematics Subject Classification. Primary 35R35, 35K55; Secondary 82C22. The work of the third author was partially funded through grant DMS-1351653 from the US National Science Foundation.

Publisher Copyright:
© 2021 American Mathematical Society. All rights reserved.

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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