{
  "id": "2311.06660",
  "version": "v1",
  "published": "2023-11-11T20:13:16.000Z",
  "updated": "2023-11-11T20:13:16.000Z",
  "title": "On asymptotic properties of solutions to $σ$-evolution equations with general double damping",
  "authors": [
    "Tuan Anh Dao",
    "Dinh Van Duong",
    "Duc Anh Nguyen"
  ],
  "comment": "29 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we would like to consider the Cauchy problem for semi-linear $\\sigma$-evolution equations with double structural damping for any $\\sigma\\ge 1$. The main purpose of the present work is to not only study the asymptotic profiles of solutions to the corresponding linear equations but also describe large-time behaviors of globally obtained solutions to the semi-linear equations. We want to emphasize that the new contribution is to find out the sharp interplay of ``parabolic like models\" corresponding to $\\sigma_1 \\in [0,\\sigma/2)$ and ``$\\sigma$-evolution like models\" corresponding to $\\sigma_2 \\in (\\sigma/2,\\sigma]$, which together appear in an equation. In this connection, we understand clearly how each damping term influences the asymptotic properties of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-11T20:13:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35B44",
      "35L30",
      "35L56"
    ],
    "keywords": [
      "asymptotic properties",
      "evolution equations",
      "general double damping",
      "main purpose",
      "asymptotic profiles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}