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

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 u n 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.