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arXiv · 1808.04857

A simple approach to the wave uniqueness problem

Abraham Solar·Sergei Trofimchuk
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Abstract

We propose a new approach for proving uniqueness of semi-wavefronts in generally non-monotone monostable reaction-diffusion equations with distributed delay. This allows to solve an open problem concerning the uniqueness of non-monotone (hence, slowly oscillating) semi-wavefronts to the KPP-Fisher equation with delay. Similarly, a broad family of the Mackey-Glass type diffusive equations is shown to possess a unique (up to translation) semi-wavefront for each admissible speed.

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Abraham Solar, Sergei Trofimchuk. 2018-08-14. A simple approach to the wave uniqueness problem. https://doi.org/10.1016/j.jde.2018.11.012

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