The Bramson delay in the non-local Fisher-KPP equation

被引:20
作者
Bouin, Emeric [1 ]
Henderson, Christopher [2 ]
Ryzhik, Lenya [3 ]
机构
[1] Univ Paris 09, CNRS, UMR 7534, CEREMADE, Pl Marechal Lattre de Tassigny, F-75775 Paris 16, France
[2] Univ Arizona, Dept Math, Tucson, AZ 85721 USA
[3] Stanford Univ, Dept Math, Stanford, CA 94305 USA
来源
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2020年 / 37卷 / 01期
基金
欧洲研究理事会;
关键词
Reaction-diffusion equations; Logarithmic delay; Parabolic Harnack inequality; TRAVELING FRONTS; WAVE; CONVERGENCE;
D O I
10.1016/j.anihpc.2019.07.001
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the non-local Fisher-KPP equation modeling a population with individuals competing with each other for resources with a strength related to their distance, and obtain the asymptotics for the position of the invasion front starting from a localized population. Depending on the behavior of the competition kernel at infinity, the location of the front is either 2t - (3/2) log t + O(1), as in the local case, or 2t - O(t(beta)) for some explicit beta is an element of (0, 1). Our main tools here are a local-in-time Harnack inequality and an analysis of the linearized problem with a suitable moving Dirichlet boundary condition. Our analysis also yields, for any beta is an element of (0, 1), examples of Fisher-KPP type non-linearities f(beta) such that the front for the local Fisher-KPP equation with reaction term f(beta) is at 2t - O(t(beta)). (C) 2019 Published by Elsevier Masson SAS.
引用
收藏
页码:51 / 77
页数:27
相关论文
共 27 条
[1]   TRAVELING FRONTS IN CYLINDERS [J].
BERESTYCKI, H ;
NIRENBERG, L .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1992, 9 (05) :497-572
[2]   The non-local Fisher-KPP equation: travelling waves and steady states [J].
Berestycki, Henri ;
Nadin, Gregoire ;
Perthame, Benoit ;
Ryzhik, Lenya .
NONLINEARITY, 2009, 22 (12) :2813-2844
[3]  
Bouin E., 2016, PREPRINT
[4]  
BRAMSON M, 1983, MEM AM MATH SOC, V44, P1
[5]   MAXIMAL DISPLACEMENT OF BRANCHING BROWNIAN-MOTION [J].
BRAMSON, MD .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1978, 31 (05) :531-581
[6]   SPATIAL STRUCTURES AND PERIODIC TRAVELING WAVES IN AN INTEGRODIFFERENTIAL REACTION-DIFFUSION POPULATION-MODEL [J].
BRITTON, NF .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1990, 50 (06) :1663-1688
[7]  
Dennis B, 2006, ECOL MONOGR, V76, P323, DOI 10.1890/0012-9615(2006)76[323:EDDPNA]2.0.CO
[8]  
2
[9]   On the large time behaviour of the multi-dimensional Fisher-KPP equation with compactly supported initial data [J].
Ducrot, Arnaud .
NONLINEARITY, 2015, 28 (04) :1043-1076
[10]   Monotone wavefronts of the nonlocal Fisher-KPP equation [J].
Fang, Jian ;
Zhao, Xiao-Qiang .
NONLINEARITY, 2011, 24 (11) :3043-3054