{
  "id": "1604.03825",
  "version": "v1",
  "published": "2016-04-13T15:20:28.000Z",
  "updated": "2016-04-13T15:20:28.000Z",
  "title": "Symmetrization and anti-symmetrization in parabolic equations",
  "authors": [
    "Luca Rossi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We derive some symmetrization and anti-symmetrization properties of parabolic equations. First, we deduce from a result by Jones a quantitative estimate of how far the level sets of solutions are from being spherical. Next, using this property, we derive a criterion providing solutions whose level sets do not converge to spheres for a class of equations including linear equations and Fisher-KPP reaction-diffusion equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-13T15:20:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K10",
      "35B06",
      "35B40"
    ],
    "keywords": [
      "parabolic equations",
      "level sets",
      "fisher-kpp reaction-diffusion equations",
      "linear equations",
      "anti-symmetrization properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}