{
  "id": "1501.02042",
  "version": "v1",
  "published": "2015-01-09T04:29:31.000Z",
  "updated": "2015-01-09T04:29:31.000Z",
  "title": "Fredholm Transform and Local Rapid Stabilization for a Kuramoto-Sivashinsky Equation",
  "authors": [
    "Jean-Michel Coron",
    "Qi Lu"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper is devoted to the study of the local rapid exponential stabilization problem for a controlled Kuramoto-Sivashinsky equation on a bounded interval. We build a feedback control law to force the solution of the closed-loop system to decay exponentially to zero with arbitrarily prescribed decay rates, provided that the initial datum is small enough. Our approach uses a method we introduced for the rapid stabilization of a Korteweg-de Vries equation. It relies on the construction of a suitable integral transform and can be applied to many other equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-09T04:29:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93D15",
      "35Q53"
    ],
    "keywords": [
      "local rapid stabilization",
      "kuramoto-sivashinsky equation",
      "fredholm transform",
      "local rapid exponential stabilization problem",
      "korteweg-de vries equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}