{
  "id": "1306.3322",
  "version": "v1",
  "published": "2013-06-14T08:04:31.000Z",
  "updated": "2013-06-14T08:04:31.000Z",
  "title": "Backward Uniqueness for Parabolic Operators with Variable Coefficients in a Half Space",
  "authors": [
    "Jie Wu",
    "Liqun Zhang"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "It is shown that a function $u$ satisfying $|\\partial_tu+\\sum_{i,j}\\partial_i(a^{ij}\\partial_ju)|\\leq N(|u|+|\\nabla u|)$, $|u(x,t)|\\leq Ne^{N|x|^2}$ in $\\mathbb{R}^n_+\\times[0,T]$ and $u(x,0)=0$ in $\\mathbb{R}^n_+$ under certain conditions on $\\{a^{ij}\\}$ must vanish identically in $\\mathbb{R}^n_+\\times[0,T]$. The main point of the result is that the conditions imposed on $\\{a^{ij}\\}$ are of the type: $\\{a^{ij}\\}$ are Lipschitz and $|\\nabla_xa^{ij}(x,t)|\\leq \\frac{E}{|x|}$, where $E$ is less than a given number, and the conditions are in some sense optimal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-14T08:04:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A02"
    ],
    "keywords": [
      "parabolic operators",
      "half space",
      "variable coefficients",
      "backward uniqueness",
      "conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.3322W"
    }
  }
}