A NOTE ON MONOTONE ITERATION METHOD FOR TRAVELING WAVES OF REACTION-DIFFUSION SYSTEMS WITH TIME DELAY

Wenzhang Huang; Yinshu Wu

doi:10.11948/2014014

2014 Volume 4 Issue 3

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Wenzhang Huang, Yinshu Wu. A NOTE ON MONOTONE ITERATION METHOD FOR TRAVELING WAVES OF REACTION-DIFFUSION SYSTEMS WITH TIME DELAY[J]. Journal of Applied Analysis & Computation, 2014, 4(3): 283-294. doi: 10.11948/2014014

Citation:

Wenzhang Huang, Yinshu Wu. A NOTE ON MONOTONE ITERATION METHOD FOR TRAVELING WAVES OF REACTION-DIFFUSION SYSTEMS WITH TIME DELAY[J]. Journal of Applied Analysis & Computation, 2014, 4(3): 283-294. doi: 10.11948/2014014

A NOTE ON MONOTONE ITERATION METHOD FOR TRAVELING WAVES OF REACTION-DIFFUSION SYSTEMS WITH TIME DELAY

Wenzhang Huang¹,
Yinshu Wu²

1 Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USA;
2 Department of Mathematics, Alabama A & M University, Huntsville, AL 35810, USA

Abstract

Abstract

For a monotone reaction-diffusion system with or without time delay, a standard approach to show the existence of a mono-stable traveling wave solution is the monotone iteration that requires the construction of a pair of upper and lower solution. In this note we will show that the monotone iteration approach can be improved by just constructing an upper solution. This improvement gives more freedom for the construction of an upper solution.
- Reaction-diffusion system /
- time delay /
- traveling waves /
- monotone iteration
MSC: 34K;35K

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References

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