{
  "id": "1911.06563",
  "version": "v1",
  "published": "2019-11-15T10:59:54.000Z",
  "updated": "2019-11-15T10:59:54.000Z",
  "title": "Some $L^1$-$L^1$ estimates for solutions to visco-elastic damped $σ$-evolution models",
  "authors": [
    "Tuan Anh Dao"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This note is to conclude $L^1-L^1$ estimates for solutions to the following Cauchy problem for visco-elastic damped $\\sigma$-evolution models: \\begin{equation} \\begin{cases} u_{tt}+ (-\\Delta)^\\sigma u+ (-\\Delta)^\\sigma u_t = 0, &\\quad x\\in \\mathbb{R}^n,\\, t \\ge 0, \\\\ u(0,x)= u_0(x),\\quad u_t(0,x)=u_1(x), &\\quad x\\in \\mathbb{R}^n, \\label{pt1.1} \\end{cases} \\end{equation} where $\\sigma> 1$, in all space dimensions $n\\ge 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-15T10:59:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L30",
      "35R11"
    ],
    "keywords": [
      "evolution models",
      "visco-elastic",
      "cauchy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}