{
  "id": "1310.5995",
  "version": "v1",
  "published": "2013-10-22T17:50:58.000Z",
  "updated": "2013-10-22T17:50:58.000Z",
  "title": "A note on the existence of non-monotone non-oscillating wavefronts",
  "authors": [
    "Anatoli Ivanov",
    "Carlos Gomez",
    "Sergei Trofimchuk"
  ],
  "comment": "11 pages, 3 figures, submitted",
  "journal": "Journal of Mathematical Analysis and Applications 419 (2014) 606-616",
  "doi": "10.1016/j.jmaa.2014.04.075",
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-22T17:50:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "45G10",
      "34K12",
      "92D25"
    ],
    "keywords": [
      "non-monotone non-oscillating wavefronts",
      "unimodal birth function",
      "mackey-glass type diffusive equations",
      "single delay",
      "monostable delayed reaction-diffusion equation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.5995I"
    }
  }
}