Global existence for a free boundary problem of Fisher–KPP type

Abstract

Motivated by the study of branching particle systems with selection, we establish global existence for the solution of the free boundary problem when the initial condition is non-increasing with as and as . We construct the solution as the limit of a sequence , where each un is the solution of a Fisher–KPP equation with the same initial condition, but with a different nonlinear term. Recent results of De Masi A et al (2017 (arXiv:1707.00799)) show that this global solution can be identified with the hydrodynamic limit of the so-called N-BBM, i.e. a branching Brownian motion in which the population size is kept constant equal to N by removing the leftmost particle at each branching event.