Convergence to a single wave in the Fisher-KPP equation

Journal Article (Journal Article)

© 2017, Fudan University and Springer-Verlag Berlin Heidelberg. The authors study the large time asymptotics of a solution of the Fisher-KPP reaction-diffusion equation, with an initial condition that is a compact perturbation of a step function. A well-known result of Bramson states that, in the reference frame moving as 2t−(3/2)log t+x∞, the solution of the equation converges as t → +∞ to a translate of the traveling wave corresponding to the minimal speed c* = 2. The constant x∞ depends on the initial condition u(0, x). The proof is elaborate, and based on probabilistic arguments. The purpose of this paper is to provide a simple proof based on PDE arguments.

Full Text

Duke Authors

Cited Authors

  • Nolen, J; Roquejoffre, JM; Ryzhik, L

Published Date

  • March 1, 2017

Published In

Volume / Issue

  • 38 / 2

Start / End Page

  • 629 - 646

Electronic International Standard Serial Number (EISSN)

  • 1860-6261

International Standard Serial Number (ISSN)

  • 0252-9599

Digital Object Identifier (DOI)

  • 10.1007/s11401-017-1087-4

Citation Source

  • Scopus