{
  "id": "1906.04471",
  "version": "v1",
  "published": "2019-06-11T10:04:03.000Z",
  "updated": "2019-06-11T10:04:03.000Z",
  "title": "Study of semi-linear $σ$-evolution equations with frictional and visco-elastic damping",
  "authors": [
    "Hironori Michihisa",
    "Tuan Anh Dao"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article, we study semi-linear $\\sigma$-evolution equations with double damping including frictional and visco-elastic damping for any $\\sigma\\ge 1$. We are interested in investigating not only higher order asymptotic expansions of solutions but also diffusion phenomenon in the $L^p-L^q$ framework, with $1\\le p\\le q\\le \\infty$, to the corresponding linear equations. By assuming additional $L^{m}$ regularity on the initial data, with $m\\in [1,2)$, we prove the global (in time) existence of small data energy solutions and indicate the large time behavior of the global obtained solutions as well to semi-linear equations. Moreover, we also determine the so-called critical exponent when $\\sigma$ is integers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-11T10:04:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35G25",
      "35B40",
      "35B33",
      "35C20"
    ],
    "keywords": [
      "evolution equations",
      "visco-elastic damping",
      "frictional",
      "small data energy solutions",
      "higher order asymptotic expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}