Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays

Zhi Cheng Wang, Wan Tong Li, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

212 Scopus citations

Abstract

This paper deals with the existence of travelling wave fronts in reaction-diffusion systems with spatio-temporal delays. Our approach is to use monotone iterations and a nonstandard ordering for the set of profiles of the corresponding wave system. New iterative techniques are established for a class of integral operators when the reaction term satisfies different monotonicity conditions. Following this, the existence of travelling wave fronts for reaction-diffusion systems with spatio-temporal delays is established. Finally, we apply the main results to a single-species diffusive model with spatio-temporal delay and obtain some existence criteria of travelling wave fronts by choosing different kernels.

Original languageEnglish (US)
Pages (from-to)185-232
Number of pages48
JournalJournal of Differential Equations
Volume222
Issue number1
DOIs
StatePublished - Mar 1 2006

Keywords

  • 34K10
  • 35B20
  • 35K57
  • Integral operator
  • Iterative techniques
  • Quasimonotonicity
  • Reaction-diffusion systems
  • Spatio-temporal delays
  • Travelling wave fronts

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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