{
  "id": "0810.2514",
  "version": "v1",
  "published": "2008-10-14T18:34:38.000Z",
  "updated": "2008-10-14T18:34:38.000Z",
  "title": "Uniqueness of self-similar solutions to the network flow in a given topological class",
  "authors": [
    "Mariel Sáez Trumper"
  ],
  "comment": "18 pages, 3 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the uniqueness of expanding self-similar solutions to the network flow in a fixed topological class. We prove the result via the parabolic Allen-Cahn approximation proved in \\cite{triodginz}. Moreover, we prove that any regular evolution of connected tree-like network (with an initial condition that might be not regular) is unique in a given a topological class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-14T18:34:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K65",
      "53C44"
    ],
    "keywords": [
      "network flow",
      "uniqueness",
      "parabolic allen-cahn approximation",
      "expanding self-similar solutions",
      "regular evolution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.2514S"
    }
  }
}