Stability of strong travelling waves for a non-local time-delayed reaction–diffusion equation
Ming Mei, Joseph W.-H. So · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2008
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.