{
  "id": "1306.4249",
  "version": "v1",
  "published": "2013-06-18T15:43:22.000Z",
  "updated": "2013-06-18T15:43:22.000Z",
  "title": "Parabolic Equation with Nonlocal Diffusion without a Smooth Inertial Manifold",
  "authors": [
    "Alexander V. Romanov"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We construct an example of a one-dimensional parabolic integro-differential equation with nonlocal diffusion which does not have asymptotically finite-dimensional dynamics in the corresponding state space. This example is more natural in the class of evolutionary equations of parabolic type than those known earlier.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-18T15:43:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B42",
      "35B40",
      "35K68"
    ],
    "keywords": [
      "smooth inertial manifold",
      "nonlocal diffusion",
      "parabolic equation",
      "one-dimensional parabolic integro-differential equation",
      "asymptotically finite-dimensional dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.4249R"
    }
  }
}