{
  "id": "1907.09299",
  "version": "v1",
  "published": "2019-07-22T13:12:56.000Z",
  "updated": "2019-07-22T13:12:56.000Z",
  "title": "Thresholds for low regularity solutions to wave equations with structural damping",
  "authors": [
    "Tomonori Fukushima",
    "Ryo Ikehata",
    "Hironori Michihisa"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the asymptotic behavior of solutions to wave equations with a structural damping term \\[ u_{tt}-\\Delta u+\\Delta^2 u_t=0, \\qquad u(0,x)=u_0(x), \\,\\,\\, u_t(0,x)=u_1(x), \\] in the whole space. New thresholds are reported in this paper that indicate which of the diffusion wave property and the non-diffusive structure dominates in low regularity cases. We develop to that end the previous author's research in 2019 where they have proposed a threshold that expresses whether the parabolic-like property or the wave-like property strongly appears in the solution to some regularity-loss type dissipative wave equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-22T13:12:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B05",
      "35B33",
      "35B40",
      "35B65",
      "35L30"
    ],
    "keywords": [
      "low regularity solutions",
      "structural damping",
      "regularity-loss type dissipative wave equation",
      "low regularity cases",
      "diffusion wave property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}