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On travelling wavefronts of Nicholson's blowflies equation with diffusion

Published online by Cambridge University Press:  04 February 2010

Chi-Kun Lin  and
Ming Mei
Chi-Kun Lin
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30010, Taiwan, ([email protected])
Ming Mei
Affiliation:
Department of Mathematics, Champlain College Saint-Lambert, Saint-Lambert, Quebec J4P 3P2, Canada, and Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3G 1M8, Canada, ([email protected]; [email protected])
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Abstract

This paper is devoted to the study of Nicholson's blowflies equation with diffusion: a kind of time-delayed reaction diffusion. For any travelling wavefront with speed c > c* (c* is the minimum wave speed), we prove that the wavefront is time-asymptotically stable when the delay-time is sufficiently small, and the initial perturbation around the wavefront decays to zero exponentially in space as x → −∞, but it can be large in other locations. The result develops and improves the previous wave stability obtained by Mei et al. in 2004. The new approach developed in this paper is the comparison principle combined with the technical weighted-energy method. Numerical simulations are also carried out to confirm our theoretical results.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 1 , February 2010 , pp. 135 - 152
Copyright
Copyright © Royal Society of Edinburgh 2010

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