### Abstract

Original language | English |
---|---|

Pages (from-to) | 3912-3939 |

Number of pages | 29 |

Journal | Nonlinearity |

Volume | 32 |

Issue number | 10 |

DOIs | |

Publication status | Published - 12 Sep 2019 |

### Cite this

*Nonlinearity*,

*32*(10), 3912-3939. https://doi.org/10.1088/1361-6544/ab25af

**Global existence for a free boundary problem of Fisher-KPP type.** / Berestycki, Julien ; Brunet, Éric; Penington, Sarah.

Research output: Contribution to journal › Article

*Nonlinearity*, vol. 32, no. 10, pp. 3912-3939. https://doi.org/10.1088/1361-6544/ab25af

}

TY - JOUR

T1 - Global existence for a free boundary problem of Fisher-KPP type

AU - Berestycki, Julien

AU - Brunet, Éric

AU - Penington, Sarah

PY - 2019/9/12

Y1 - 2019/9/12

N2 - 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.

AB - 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.

U2 - 10.1088/1361-6544/ab25af

DO - 10.1088/1361-6544/ab25af

M3 - Article

VL - 32

SP - 3912

EP - 3939

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 10

ER -