{
  "id": "1903.11939",
  "version": "v1",
  "published": "2019-03-28T13:12:48.000Z",
  "updated": "2019-03-28T13:12:48.000Z",
  "title": "Time-fractional equations with reaction terms: fundamental solutions and asymptotics",
  "authors": [
    "Serena Dipierro",
    "Benedetta Pellacci",
    "Enrico Valdinoci",
    "Gianmaria Verzini"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We analyze the fundamental solution of a time-fractional problem, establishing existence and uniqueness in an appropriate functional space. We also focus on the one-dimensional spatial setting in the case in which the time-fractional exponent is equal to, or larger than, $\\frac12$. In this situation, we prove that the speed of invasion of the fundamental solution is at least `almost of square root type', namely it is larger than~$ct^\\beta$ for any given~$c>0$ and~$\\beta\\in\\left(0,\\frac12\\right)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-28T13:12:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental solution",
      "time-fractional equations",
      "reaction terms",
      "asymptotics",
      "square root type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}