{
  "id": "2401.03837",
  "version": "v1",
  "published": "2024-01-08T11:51:14.000Z",
  "updated": "2024-01-08T11:51:14.000Z",
  "title": "Reconstruction of the initial condition in parabolic equations with Log-Lipschitz coefficients",
  "authors": [
    "Daniele Del Santo",
    "Martino Prizzi"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a parabolic equation whose coefficients are Log-Lipschitz continuous in $t$ and Lipschitz continuous in $x$. Combining a recent conditional stability result with a well posed variational problem, we reconstruct the initial condition of an unknown solution from a rough measurement at the final time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-08T11:51:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B30",
      "35K10",
      "35R25"
    ],
    "keywords": [
      "parabolic equation",
      "initial condition",
      "log-lipschitz coefficients",
      "reconstruction",
      "conditional stability result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}