{
  "id": "2210.09130",
  "version": "v1",
  "published": "2022-10-17T14:29:18.000Z",
  "updated": "2022-10-17T14:29:18.000Z",
  "title": "Exact controllability and stabilization for linear dispersive PDE's on the two-dimensional torus",
  "authors": [
    "Francisco J. Vielma Leal",
    "Ademir Pastor"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE's posed on the two-dimensional torus $\\mathbb{T}^{2}.$ The control function is considered to be acting on a small vertical and horizontal strip of the torus. Our results apply to several well-known models including some bidimesional extensions of the Benajamin-Ono and Korteweg-de Vries equations. As a by product, the exponential stabilizability with any given decay rate is also established in $H^{s}_{p}(\\mathbb{T}^{2}),$ with $s\\geq 0,$ by constructing an appropriated feedback control law.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-17T14:29:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exact controllability",
      "two-dimensional torus",
      "stabilization",
      "bidimensional linear dispersive pdes",
      "korteweg-de vries equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}