{
  "id": "1303.6834",
  "version": "v2",
  "published": "2013-03-27T14:04:05.000Z",
  "updated": "2014-01-02T22:46:44.000Z",
  "title": "Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system",
  "authors": [
    "Sébastien Court"
  ],
  "comment": "37 pages, 1 figure",
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "In this second part we prove that the full nonlinear fluid-solid system introduced in Part I is stabilizable by deformations of the solid that have to satisfy nonlinear constraints. Some of these constraints are physical and guarantee the self-propelled nature of the solid. The proof is based on the boundary feedback stabilization of the linearized system. From this boundary feedback operator we construct a deformation of the solid which satisfies the aforementioned constraints and which stabilizes the nonlinear system. The proof is made by a fixed point method.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-02T22:46:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93C20",
      "35Q30",
      "76D05",
      "76D07",
      "74F10",
      "93C05",
      "93B52",
      "93D15",
      "74A99",
      "35Q74"
    ],
    "keywords": [
      "nonlinear system",
      "self-propelled solid",
      "deformation",
      "full nonlinear fluid-solid system",
      "satisfy nonlinear constraints"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.6834C"
    }
  }
}