{
  "id": "1402.5009",
  "version": "v1",
  "published": "2014-02-20T14:29:30.000Z",
  "updated": "2014-02-20T14:29:30.000Z",
  "title": "Long-time behavior of solutions of a BBM equation with generalized damping",
  "authors": [
    "Jean-Paul Chehab",
    "Pierre Garnier",
    "Youcef Mammeri"
  ],
  "categories": [
    "math.AP",
    "math.NA"
  ],
  "abstract": "We study the long-time behavior of the solution of a damped BBM equation $u_t + u_x - u_{xxt} + uu_x + \\mathscr{L}_{\\gamma}(u) = 0$. The proposed dampings $\\mathscr{L}_{\\gamma}$ generalize standards ones, as parabolic ($\\mathscr{L}_{\\gamma}(u)=-\\Delta u$) or weak damping ($\\mathscr{L}_{\\gamma}(u)=\\gamma u$) and allows us to consider a greater range. After establish the local well-posedness in the energy space, we investigate some numerical properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-20T14:29:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long-time behavior",
      "generalized damping",
      "damped bbm equation",
      "greater range",
      "local well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.5009C"
    }
  }
}