{
  "id": "1309.7634",
  "version": "v2",
  "published": "2013-09-29T18:07:04.000Z",
  "updated": "2014-03-24T15:05:08.000Z",
  "title": "Existence, uniqueness and decay rates for evolution equations on trees",
  "authors": [
    "Leandro M. Del Pezzo",
    "Carolina A. Mosquera",
    "Julio D. Rossi"
  ],
  "comment": "11 pages. Keywords: Evolution equations, averaging operators, decay estimates. arXiv admin note: text overlap with arXiv:1303.6521",
  "journal": "Portugaliae Mathematica, Vol. 71, Fasc. 1, 2014, 63-77",
  "doi": "10.4171/PM/1941",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study evolution equations governed by an averaging operator on a directed tree, showing existence and uniqueness of solutions. In addition we find conditions of the initial condition that allows us to find the asymptotic decay rate of the solutions as $t\\to \\infty$. It turns out that this decay rate is not uniform, it strongly depends on how the initial condition goes to zero as one goes down in the tree.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-24T15:05:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35K55",
      "91A22"
    ],
    "keywords": [
      "uniqueness",
      "initial condition",
      "asymptotic decay rate",
      "study evolution equations",
      "averaging operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7634D"
    }
  }
}