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Stability of strong travelling waves for a non-local time-delayed reaction–diffusion equation

Published online by Cambridge University Press:  14 July 2008

Ming Mei  and
Joseph W.-H. So
Ming Mei
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3A 2K6, Canada and Department of Mathematics, Champlain College, Saint-Lambert, Quebec J4P 3P2, Canada (mei@math.mcgill.ca)
Joseph W.-H. So
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada (joseph.so@ualberta.ca)
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Abstract

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The paper is concerned with a non-local time-delayed reaction–diffusion equation. We prove the (time) asymptotic stability of a travelling wavefront without a smallness assumption on its wavelength, i.e. the so-called strong wavefront, by means of the (technical) weighted energy method, when the initial perturbation around the wave is small. The exponential convergent rate is also given. Selection of a suitable weight plays a key role in the proof.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 3 , June 2008 , pp. 551 - 568
Copyright
2008 Royal Society of Edinburgh