{
  "id": "2009.06395",
  "version": "v1",
  "published": "2020-09-11T02:33:29.000Z",
  "updated": "2020-09-11T02:33:29.000Z",
  "title": "Asymptotic profiles for a wave equation with parameter dependent logarithmic damping",
  "authors": [
    "Ruy Coimbra Charao",
    "Marcello D'Abbicco",
    "Ryo Ikehata"
  ],
  "comment": "20 pages. arXiv admin note: text overlap with arXiv:2002.06319",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study a nonlocal wave equation with logarithmic damping which is rather weak in the low frequency zone as compared with frequently studied strong damping case. We consider the Cauchy problem for this model in the whole space and we study the asymptotic profile and optimal estimates of the solutions and the total energy as time goes to infinity in L^{2}-sense. In that case some results on hypergeometric functions are useful.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-11T02:33:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35B40",
      "35B05",
      "35B45",
      "35C20",
      "35S05"
    ],
    "keywords": [
      "parameter dependent logarithmic damping",
      "asymptotic profile",
      "low frequency zone",
      "nonlocal wave equation",
      "strong damping case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}