{
  "id": "1109.3863",
  "version": "v1",
  "published": "2011-09-18T12:05:25.000Z",
  "updated": "2011-09-18T12:05:25.000Z",
  "title": "An observability for parabolic equations from a measurable set in time",
  "authors": [
    "Kim Dang Phung",
    "Gengsheng Wang"
  ],
  "categories": [
    "math.AP",
    "cs.SY",
    "math.OC"
  ],
  "abstract": "This paper presents a new observability estimate for parabolic equations in $\\Omega\\times(0,T)$, where $\\Omega$ is a convex domain. The observation region is restricted over a product set of an open nonempty subset of $\\Omega$ and a subset of positive measure in $(0,T)$. This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-18T12:05:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parabolic equations",
      "measurable set",
      "time optimal control problems",
      "open nonempty subset",
      "convex domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.3863D"
    }
  }
}