{
  "id": "2401.16377",
  "version": "v1",
  "published": "2024-01-29T18:16:29.000Z",
  "updated": "2024-01-29T18:16:29.000Z",
  "title": "Large time behaviour for the heat equation on $\\Z,$ moments and decay rates",
  "authors": [
    "Luciano Abadias",
    "Jorge González-Camus",
    "Pedro J. Miana",
    "Juan C. Pozo"
  ],
  "comment": "pp 25",
  "journal": "JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021",
  "categories": [
    "math.AP",
    "math.DS",
    "math.FA"
  ],
  "abstract": "The paper is devoted to understand the large time behaviour and decay of the solution of the discrete heat equation in the one dimensional mesh $\\Z$ on $\\ell^p$ spaces, and its analogies with the continuous-space case. We do a deep study of the moments of the discrete gaussian kernel (which is given in terms of Bessel functions), in particular the mass conservation principle; that is reflected on the large time behaviour of solutions. We prove asymptotic pointwise and $\\ell^p$ decay results for the fundamental solution. We use that estimates to get rates on the $\\ell^p$ decay and large time behaviour of solutions. For the $\\ell^2$ case, we get optimal decay by use of Fourier techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-29T18:16:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35A08",
      "33C10",
      "39A12"
    ],
    "keywords": [
      "large time behaviour",
      "decay rates",
      "discrete heat equation",
      "mass conservation principle",
      "discrete gaussian kernel"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}