{
  "id": "1605.09574",
  "version": "v1",
  "published": "2016-05-31T10:56:19.000Z",
  "updated": "2016-05-31T10:56:19.000Z",
  "title": "On the Benjamin-Bona-Mahony equation with a localized damping",
  "authors": [
    "Lionel Rosier"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We introduce several mechanisms to dissipate the energy in the Benjamin-Bona-Mahony (BBM) equation. We consider either a distributed (localized) feedback law, or a boundary feedback law. In each case, we prove the global wellposedness of the system and the convergence towards a solution of the BBM equation which is null on a band. If the Unique Continuation Property holds for the BBM equation, this implies that the origin is asymp-totically stable for the damped BBM equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-31T10:56:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "benjamin-bona-mahony equation",
      "localized damping",
      "unique continuation property holds",
      "boundary feedback law",
      "global wellposedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}