{
  "id": "1601.06271",
  "version": "v1",
  "published": "2016-01-23T14:28:44.000Z",
  "updated": "2016-01-23T14:28:44.000Z",
  "title": "Minimisers of the Allen-Cahn equation on hyperbolic graphs",
  "authors": [
    "Blaz Mramor"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1508.06751",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate minimal solutions of the Allen-Cahn equation on a Gromov-hyperbolic graph. Under some natural conditions on the graph, we show the existence of non-constant uniformly-bounded minimal solutions with prescribed asymptotic behaviours. For a phase field model on a hyperbolic graph, such solutions describe energy-minimising steady-state phase transitions that converge towards prescribed phases given by the asymptotic directions on the graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-23T14:28:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J05",
      "35J20",
      "53C23"
    ],
    "keywords": [
      "allen-cahn equation",
      "minimisers",
      "energy-minimising steady-state phase transitions",
      "non-constant uniformly-bounded minimal solutions",
      "phase field model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160106271M"
    }
  }
}