A free boundary problem arising from branching Brownian motion with selection

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 model which is studied in the companion paper (see Julien Berestycki, Éric Brunet, James Nolen, and Sarah Penington [, 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.

Duke Scholars

Author James H. Nolen Mathematics