American Institute of Mathematical Sciences

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July  2003, 9(4): 925-936. doi: 10.3934/dcds.2003.9.925

Existence of traveling wavefronts of delayed reaction diffusion systems without monotonicity

Jianhua Huang 1, and  Xingfu Zou 2,

1. 

Dept. Math., Central China Normal University, Wuhan, HuBei 430079, China
2. 

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, A1C5S7, Canada

Received  November 2001 Revised  November 2002 Published  April 2003

In this paper, we establish the existence of traveling wavefronts for delayed reaction diffusion systems without quasimonotonicity in the reaction term, by using Schauder's fixed point theorem. We show the merit of our result by applying it to the Belousov-Zhabotinskii reaction model with two delays.
Keywords: Traveling wavefront, reaction diffusion systems, quasimonotone, delay, upper solution and lower solution., Schauder’s fixed point theorem.
Mathematics Subject Classification: 34K10, 35B20, 35K5.
Citation: Jianhua Huang, Xingfu Zou. Existence of traveling wavefronts of delayed reaction diffusion systems without monotonicity. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 925-936. doi: 10.3934/dcds.2003.9.925
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