Sharp large time behaviour in N -dimensional Fisher-KPP equations
Analysis of PDEs
2019-03-28 v1
Abstract
We study the large time behaviour of the Fisher-KPP equation t u = u + u -- u 2 in spatial dimension N , when the initial datum is compactly supported. We prove the existence of a Lipschitz function s of the unit sphere, such that u(t, x) converges, as t goes to infinity, to U c * |x| -- c * t + N + 2 c * lnt + s x |x| , where U c * is the 1D travelling front with minimal speed c * = 2. This extends an earlier result of G{\"a}rtner.
Cite
@article{arxiv.1903.11274,
title = {Sharp large time behaviour in N -dimensional Fisher-KPP equations},
author = {Jean-Michel Roquejoffre and Luca Rossi and Violaine Roussier-Michon},
journal= {arXiv preprint arXiv:1903.11274},
year = {2019}
}