On the existence of non-monotone non-oscillating wavefronts

Anatoli Ivanov, Carlos Gomez, Sergei Trofimchuk

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Abstract

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 et al. and Ducrot et al., the same question has a negative answer for the KPP-Fisher equation with a single delay.

Original languageEnglish (US)
Pages (from-to)606-616
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume419
Issue number1
DOIs
Publication statusPublished - Nov 1 2014

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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