{
  "id": "1611.09955",
  "version": "v1",
  "published": "2016-11-30T00:41:15.000Z",
  "updated": "2016-11-30T00:41:15.000Z",
  "title": "Inverse problems for parabolic equations 3",
  "authors": [
    "A. G. Ramm"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $u_t-a(t)u_{xx}=f(x, t)$ in $0\\leq x \\leq \\pi,\\,\\,t\\geq 0.$ Assume that $u(0,t)=u_1(t)$, $u(\\pi,t)=u_2(t)$, $u(x,0)=h(x)$, and the extra data $u_x(0,t)=g(t)$ are known. The inverse problem is: {\\it How does one determine the unknown $a(t)$?} The function $a(t)>a_0>0$ is assumed continuous and bounded. This question is answered and a method for recovery of $a(t)$ is proposed. There are several papers in which sufficient conditions are given for the uniqueness and existence of $a(t)$, but apparently there was no method proposed for calculating of $a$. The method given in this paper for proving the uniqueness and existence of the solution to inverse problem is new and it allows one to calculate the unknown coefficient $a(t)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-30T00:41:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K20",
      "35R30"
    ],
    "keywords": [
      "inverse problem",
      "parabolic equations",
      "extra data",
      "sufficient conditions",
      "uniqueness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}