{
  "id": "2204.11342",
  "version": "v1",
  "published": "2022-04-24T19:37:09.000Z",
  "updated": "2022-04-24T19:37:09.000Z",
  "title": "Decay/growth rates for inhomogeneous heat equations with memory. The case of small dimensions",
  "authors": [
    "Carmen Cortázar",
    "Fernando Quirós",
    "Noemí Wolanski"
  ],
  "comment": "17 pages. arXiv admin note: text overlap with arXiv:2107.01741",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the decay/growth rates in all $L^p$ norms of solutions to an inhomogeneous nonlocal heat equation in $\\mathbb{R}^N$ involving a Caputo $\\alpha$-time derivative and a power $\\beta$ of the Laplacian when the spatial dimension is small, $1\\le N\\le 4\\beta$, thus completing the already available results for large spatial dimensions. Rates depend not only on $p$, but also on the space-time scale and on the time behavior of the spatial $L^1$ norm of the forcing term.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-24T19:37:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35R11",
      "35R09",
      "45K05"
    ],
    "keywords": [
      "inhomogeneous heat equations",
      "decay/growth rates",
      "small dimensions",
      "inhomogeneous nonlocal heat equation",
      "large spatial dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}