1. A free boundary problem arising from branching Brownian motion with selection
- Author
-
Sarah Penington, James Nolen, Éric Brunet, and Julien Berestycki
- Subjects
Mathematics(all) ,Interacting particle system ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Probability (math.PR) ,35R35, 35K55, 82C22 ,Boundary (topology) ,01 natural sciences ,Parabolic partial differential equation ,Constraint (information theory) ,Mathematics - Analysis of PDEs ,Free boundary problem ,FOS: Mathematics ,Uniqueness ,Limit (mathematics) ,0101 mathematics ,Mathematics - Probability ,Brownian motion ,Mathematics ,Analysis of PDEs (math.AP) - 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 a companion paper. 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., Comment: 53 pages
- Published
- 2021