A free boundary problem arising from branching Brownian motion with selection
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- by Julien Berestycki, Éric Brunet, James Nolen and Sarah Penington PDF
- Trans. Amer. Math. Soc. 374 (2021), 6269-6329 Request permission
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.References
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Additional Information
- Julien Berestycki
- Affiliation: Department of Statistics, University of Oxford, United Kingdom
- MR Author ID: 711968
- ORCID: 0000-0001-8783-4937
- Éric Brunet
- Affiliation: Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS Sorbonne Université, Université de Paris, F-75005 Paris, France
- James Nolen
- Affiliation: Department of Mathematics, Duke University, Box 90320, Durham, North Carolina 27708
- MR Author ID: 727616
- ORCID: 0000-0003-4630-2293
- Sarah Penington
- Affiliation: Department of Mathematical Sciences, University of Bath, United Kingdom
- MR Author ID: 1207094
- ORCID: 0000-0001-5348-7295
- Received by editor(s): June 23, 2020
- Received by editor(s) in revised form: November 17, 2020
- Published electronically: May 18, 2021
- Additional Notes: The work of the third author was partially funded through grant DMS-1351653 from the US National Science Foundation.
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 6269-6329
- MSC (2020): Primary 35R35, 35K55; Secondary 82C22
- DOI: https://doi.org/10.1090/tran/8370
- MathSciNet review: 4302161