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

Shangjiang Guo, Johannes Zimmer

Research output: Contribution to journalArticle

14 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
DOIs
Publication statusPublished - Feb 2015

Fingerprint

Nonlocal Delay
Traveling Wavefronts
reaction-diffusion equations
energy methods
Discrete Equations
Wavefronts
Reaction-diffusion Equations
Wave Front
infinity
Green's functions
time lag
perturbation
decay
Energy Method
Green's function
Time Delay
Infinity
Decay
Perturbation
Time delay

Keywords

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

Cite this

Stability of travelling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects. / Guo, Shangjiang; Zimmer, Johannes.

In: Nonlinearity, Vol. 28, No. 2, 02.2015, p. 463-492.

Research output: Contribution to journalArticle

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