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Traveling Wave Fronts of Reaction-Diffusion Systems with Delay

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An Erratum to this article was published on 02 November 2007

Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, York University, North York, Ontario, Canada, M3J 1P3

    Jianhong Wu

  2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, Canada, A1C 5S7

    Xingfu Zou

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  1. Jianhong Wu
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An erratum to this article is available at http://dx.doi.org/10.1007/s10884-007-9090-1.

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Wu, J., Zou, X. Traveling Wave Fronts of Reaction-Diffusion Systems with Delay. Journal of Dynamics and Differential Equations 13, 651–687 (2001). https://doi.org/10.1023/A:1016690424892

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