{
  "id": "1908.08492",
  "version": "v1",
  "published": "2019-08-22T16:57:35.000Z",
  "updated": "2019-08-22T16:57:35.000Z",
  "title": "Some remarks on the asymptotic profile of solutions to structurally damped $σ$-evolution equations",
  "authors": [
    "Tuan Anh Dao"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we are interested in analyzing the asymptotic profiles of solutions to the Cauchy problem for linear structurally damped $\\sigma$-evolution equations in $L^2$-sense. Depending on the parameters $\\sigma$ and $\\delta$ we would like to not only indicate approximation formula of solutions but also recognize the optimality of their decay rates as well in the distinct cases of parabolic like damping and $\\sigma$-evolution like damping. Moreover, such results are also discussed when we mix these two kinds of damping terms in a $\\sigma$-evolution equation to investigate how each of them affects the asymptotic profile of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-22T16:57:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35L30",
      "35G10",
      "35M11"
    ],
    "keywords": [
      "evolution equation",
      "asymptotic profile",
      "decay rates",
      "distinct cases",
      "cauchy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}