Traveling Wave Fronts of Reaction-Diffusion Systems with Delay |
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Authors: | Jianhong Wu Xingfu Zou |
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Institution: | (1) Department of Mathematics and Statistics, York University, North York, Ontario, Canada, M3J 1P3;(2) Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, Canada, A1C 5S7 |
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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.
An erratum to this article is available at . |
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Keywords: | traveling wave fronts reaction-diffusion systems with delay monotone iteration nonstandard ordering quasimonotonicity nonquasimonotonicity |
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