{
  "id": "2307.04697",
  "version": "v1",
  "published": "2023-07-10T16:54:25.000Z",
  "updated": "2023-07-10T16:54:25.000Z",
  "title": "On the time behavior of a porous thermoelastic system with only thermal dissipation given by Gurtin-Pipkin law",
  "authors": [
    "Afaf Ahmima",
    "Abdelfeteh Fareh"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In the present paper we consider a porous thermoelastic system with only one dissipative mechanism generated by the heat conductivity modelled by the Gurtin-Pipkin thermal law. By the use of a semigroup approach and the Lumer-Phillips theorem we prove the existence of a unique solution. We introduce a stability number $\\chi_g$ depends on the coefficients of the system, and establish an exponential stability result provided that $\\chi_g=0$. Otherwise, if $\\chi_g\\ne 0$, we prove the lack of exponential decay. Our result improves and generalizes the previous results in the literature obtained for Fourier's and Cattaneo's laws of thermal conductivity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-10T16:54:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "47D03",
      "74D05",
      "74F15"
    ],
    "keywords": [
      "porous thermoelastic system",
      "thermal dissipation",
      "gurtin-pipkin law",
      "time behavior",
      "gurtin-pipkin thermal law"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}