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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
Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3A 2K6, Canada and Department of Mathematics, Champlain College, Saint-Lambert, Quebec J4P 3P2, Canada (
Joseph W.-H. So
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada (


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.

Research Article
2008 Royal Society of Edinburgh

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