{
  "id": "2107.01741",
  "version": "v1",
  "published": "2021-07-04T22:09:43.000Z",
  "updated": "2021-07-04T22:09:43.000Z",
  "title": "Decay/growth rates for inhomogeneous heat equations with memory. The case of large dimensions",
  "authors": [
    "Carmen Cortázar",
    "Fernando Quirós",
    "Noemí Wolanski"
  ],
  "comment": "16 pages, 1 figure",
  "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 dimension is large, $N> 4\\beta$. Rates depend strongly on the space-time scale and on the time behavior of the spatial $L^1$ norm of the forcing term.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-04T22:09:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35R11",
      "35R09",
      "45K05"
    ],
    "keywords": [
      "inhomogeneous heat equations",
      "decay/growth rates",
      "large dimensions",
      "inhomogeneous nonlocal heat equation",
      "time behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}