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Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion

Published online by Cambridge University Press:  12 July 2007

Ming Mei ,
Joseph W.-H. So ,
Michael Y. Li  and
Samuel S.P. Shen
Ming Mei
Affiliation:
Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H3G 1M8, Canada
Joseph W.-H. So
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Michael Y. Li
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Samuel S.P. Shen
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
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Abstract

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This paper considers the nonlinear stability oftravelling wavefronts of a time-delayed diffusive Nicholson blowflies equation. We prove that, under a weighted L2 norm, ifa solution is sufficiently close to a travelling wave front initially, it converges exponentially to the wavefront as t → ∞. The rate ofconvergence is also estimated.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 3 , June 2004 , pp. 579 - 594
Copyright
Copyright © Royal Society of Edinburgh 2004