{
  "id": "1408.2020",
  "version": "v2",
  "published": "2014-08-09T04:27:20.000Z",
  "updated": "2015-01-06T08:04:16.000Z",
  "title": "On a nonlocal analog of the Kuramoto-Sivashinsky equation",
  "authors": [
    "Rafael Granero-Belinchón",
    "John K. Hunter"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a nonlocal equation, analogous to the Kuramoto-Sivashinsky equation, in which short waves are stabilized by a possibly fractional diffusion of order less than or equal to two, and long waves are destabilized by a backward fractional diffusion of lower order. We prove the global existence, uniqueness, and analyticity of solutions of the nonlocal equation and the existence of a compact attractor. Numerical results show that the equation has chaotic solutions whose spatial structure consists of interacting traveling waves resembling viscous shock profiles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-09T04:27:20.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-06T08:04:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kuramoto-sivashinsky equation",
      "nonlocal analog",
      "traveling waves resembling viscous",
      "nonlocal equation",
      "fractional diffusion"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/28/4/1103",
      "journal": "Nonlinearity",
      "year": 2015,
      "month": "Apr",
      "volume": 28,
      "number": 4,
      "pages": 1103
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015Nonli..28.1103G"
    }
  }
}