A note on the existence of non-monotone non-oscillating wavefronts
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2013
- DOI:
- 10.48550/arXiv.1310.5995
- arXiv:
- arXiv:1310.5995
- Bibcode:
- 2013arXiv1310.5995I
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- Mathematics - Analysis of PDEs;
- 45G10;
- 34K12;
- 92D25
- E-Print:
- 11 pages, 3 figures, submitted