{
  "id": "1705.02112",
  "version": "v1",
  "published": "2017-05-05T07:54:07.000Z",
  "updated": "2017-05-05T07:54:07.000Z",
  "title": "Global attractors for the Benjamin-Bona-Mahony equation with memory",
  "authors": [
    "Filippo Dell'Oro",
    "Olivier Goubet",
    "Youcef Mammeri",
    "Vittorino Pata"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the nonlinear integrodifferential Benjamin-Bona-Mahony equation $$ u_t - u_{txx} + u_x - \\int_0^\\infty g(s) u_{xx}(t-s) {\\rm d} s + u u_x = f $$ where the dissipation is entirely contributed by the memory term. Under a suitable smallness assumption on the external force $f$, we show that the related solution semigroup possesses the global attractor in the natural weak energy space. The result is obtained by means of a nonstandard approach based on the construction of a suitable family of attractors on certain invariant sets of the phase space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-05T07:54:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global attractor",
      "nonlinear integrodifferential benjamin-bona-mahony equation",
      "natural weak energy space",
      "related solution semigroup possesses",
      "phase space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}