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arXiv · 1310.5995

A note on the existence of non-monotone non-oscillating wavefronts

Anatoli Ivanov·Carlos Gomez·Sergei Trofimchuk
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Abstract

In this note, we present a monostable delayed reaction-diffusion equation with the unimodal birth function which admits only non-monotone wavefronts. Moreover, these fronts are either eventually monotone (in particular, such is the minimal wave) or slowly oscillating. Hence, for the Mackey-Glass type diffusive equations, we answer affirmatively the question about the existence of non-monotone non-oscillating wavefronts. As it was recently established by Hasik {\it et al.} and Ducrot {\it et al.}, the same question has a negative answer for the KPP-Fisher equation with a single delay.

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Anatoli Ivanov, Carlos Gomez, Sergei Trofimchuk. 2013-10-22. A note on the existence of non-monotone non-oscillating wavefronts. https://doi.org/10.1016/j.jmaa.2014.04.075

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