{
  "id": "1908.02015",
  "version": "v1",
  "published": "2019-08-06T08:37:29.000Z",
  "updated": "2019-08-06T08:37:29.000Z",
  "title": "On the identification of source term in the heat equation from sparse data",
  "authors": [
    "William Rundell",
    "Zhidong Zhang"
  ],
  "categories": [
    "math.AP",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "We consider the recovery of a source term $f(x,t)=p(x)q(t)$ for the nonhomogeneous heat equation in $\\Omega\\times (0,\\infty)$ where $\\Omega$ is a bounded domain in $\\mathbb{R}^2$ with smooth boundary $\\partial\\Omega$ from overposed lateral data on a sparse subset of $\\partial\\Omega\\times(0,\\infty)$. Specifically, we shall require a small finite number $N$ of measurement points on $\\partial\\Omega$ and prove a uniqueness result; namely the recovery of the pair $(p,q)$ within a given class, by a judicious choice of $N=2$ points. Naturally, with this paucity of overposed data, the problem is severely ill-posed. Nevertheless we shall show that provided the data noise level is low, effective numerical reconstructions may be obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-06T08:37:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "65M32"
    ],
    "keywords": [
      "source term",
      "sparse data",
      "identification",
      "data noise level",
      "small finite number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}