On the existence of non-monotone non-oscillating wavefronts |
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Authors: | Anatoli Ivanov Carlos Gomez Sergei Trofimchuk |
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Affiliation: | 1. Department of Mathematics, Pennsylvania State University, P.O. Box PSU, Lehman, PA 18627, USA;2. Instituto de Matemática y Fisica, Universidad de Talca, Casilla 747, Talca, Chile |
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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. |
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Keywords: | Monostable nonlinearity Diffusive Mackey&ndash Glass equation Delay Wavefront Non-monotone response |
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