Stability of travelling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects

Shangjiang Guo, Johannes Zimmer

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

This paper deals with travelling wavefronts for temporally delayed, spatially discrete reaction-diffusion equations. Using a combination of the weighted energy method and the Green function technique, we prove that all noncritical wavefronts are globally exponentially stable, and critical wavefronts are globally algebraically stable when the initial perturbations around the wavefront decay to zero exponentially near minus infinity regardless of the magnitude of time delay.

Original languageEnglish
Pages (from-to)463-492
Number of pages30
JournalNonlinearity
Volume28
Issue number2
Early online date16 Jan 2015
DOIs
Publication statusPublished - 28 Feb 2015

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Keywords

  • Fisher-KPP equation
  • global stability
  • Green functions
  • time delay
  • travelling waves
  • weighted energy

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