{
  "id": "0801.2678",
  "version": "v1",
  "published": "2008-01-17T14:00:38.000Z",
  "updated": "2008-01-17T14:00:38.000Z",
  "title": "On asymptotic stability in 3D of kinks for the $φ^4$ model",
  "authors": [
    "Scipio Cuccagna"
  ],
  "comment": "To appear on Transactions of the American Mathematical Society",
  "categories": [
    "math.AP"
  ],
  "abstract": "We add to a kink, which is a 1 dimensional structure, two transversal directions. We then check its asymptotic stability with respect to compactly supported perturbations in 3D and a time evolution under a Nonlinear Wave Equation (NLW). The problem is inspired by work by Jack Xin on asymptotic stability in dimension larger than 1 of fronts for reaction diffusion equations. The proof involves a separation of variables. The transversal variables are treated as in work on Nonlinear Klein Gordon Equation (NLKG) originating from Klainerman and from Shatah in a particular elaboration due to Delort and others. The longitudinal variable is treated by means of a result by Weder on dispersion for Schroedinger operators in 1D.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-17T14:00:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic stability",
      "nonlinear klein gordon equation",
      "reaction diffusion equations",
      "nonlinear wave equation",
      "dimension larger"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}