{
  "id": "2105.12800",
  "version": "v1",
  "published": "2021-05-26T19:19:53.000Z",
  "updated": "2021-05-26T19:19:53.000Z",
  "title": "Optimal Estimates on the Propagation of Reactions with Fractional Diffusion",
  "authors": [
    "Yuming Paul Zhang",
    "Andrej Zlatos"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the reaction-fractional-diffusion equation $u_t+(-\\Delta)^{s} u=f(u)$ with ignition and monostable reactions $f$, and $s\\in(0,1)$. We obtain the first optimal bounds on the propagation of front-like solutions in the cases where no traveling fronts exist. Our results cover most of these cases, and also apply to propagation from localized initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-26T19:19:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K57",
      "35B40",
      "26A33"
    ],
    "keywords": [
      "fractional diffusion",
      "optimal estimates",
      "propagation",
      "first optimal bounds",
      "reaction-fractional-diffusion equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}