{
  "id": "1809.10942",
  "version": "v1",
  "published": "2018-09-28T10:08:34.000Z",
  "updated": "2018-09-28T10:08:34.000Z",
  "title": "On null-controllability of the heat equation on infinite strips and control cost estimate",
  "authors": [
    "Michela Egidi"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider an infinite strip $\\Omega_L=(0,2\\pi L)^{d-1}\\times\\mathbb{R}$, $d\\geq 2$, $L>0$, and study the control problem of the heat equation on $\\Omega_L$ with Dirichlet or Neumann boundary conditions, and control set $\\omega\\subset\\Omega_L$. We provide a sufficient and necessary condition for null-controllability in any positive time $T>0$, which is a geometric condition on the control set $\\omega$. This is referred to as \"thickness with respect to $\\Omega_L$\" and implies that the set $\\omega$ cannot be concentrated in a particular region of $\\Omega_L$. We compare the thickness condition with a previously known necessity condition for null-controllability and give a control cost estimate which only shows dependence on the geometric parameters of $\\omega$ and the time $T$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-28T10:08:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "control cost estimate",
      "infinite strip",
      "heat equation",
      "null-controllability",
      "control set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}