{
  "id": "1607.06426",
  "version": "v1",
  "published": "2016-07-21T19:00:14.000Z",
  "updated": "2016-07-21T19:00:14.000Z",
  "title": "A concrete realization of the slow-fast alternative for a semi linear heat equation with homogeneous Neumann boundary conditions",
  "authors": [
    "Marina Ghisi",
    "Massimo Gobbino",
    "Alain Haraux"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the asymptotic behavior of solutions to a semilinear heat equation with homogeneous Neumann boundary conditions. It was recently shown that the nontrivial kernel of the linear part leads to the coexistence of fast solutions decaying to 0 exponentially (as time goes to infinity), and slow solutions decaying to 0 as negative powers of t. Here we provide a characterization of slow/fast solutions in terms of their sign, and we show that the set of initial data giving rise to fast solutions is a graph of codimension one in the phase space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-21T19:00:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K58",
      "35K90",
      "35B40"
    ],
    "keywords": [
      "homogeneous neumann boundary conditions",
      "semi linear heat equation",
      "concrete realization",
      "slow-fast alternative",
      "fast solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}