Journal of Dynamics and Differential Equations

, Volume 13, Issue 3, pp 651–687

Traveling Wave Fronts of Reaction-Diffusion Systems with Delay

  • Jianhong Wu
  • Xingfu Zou

DOI: 10.1023/A:1016690424892

Cite this article as:
Wu, J. & Zou, X. Journal of Dynamics and Differential Equations (2001) 13: 651. doi:10.1023/A:1016690424892


This paper deals with the existence of traveling wave front solutions of reaction-diffusion systems with delay. A monotone iteration scheme is established for the corresponding wave system. If the reaction term satisfies the so-called quasimonotonicity condition, it is shown that the iteration converges to a solution of the wave system, provided that the initial function for the iteration is chosen to be an upper solution and is from the profile set. For systems with certain nonquasimonotone reaction terms, a convergence result is also obtained by further restricting the initial functions of the iteration and using a non-standard ordering of the profile set. Applications are made to the delayed Fishery–KPP equation with a nonmonotone delayed reaction term and to the delayed system of the Belousov–Zhabotinskii reaction model.

traveling wave fronts reaction-diffusion systems with delay monotone iteration nonstandard ordering quasimonotonicity nonquasimonotonicity 

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Jianhong Wu
    • 1
  • Xingfu Zou
    • 2
  1. 1.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada
  2. 2.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John'sCanada

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