{
  "id": "2005.04524",
  "version": "v1",
  "published": "2020-05-09T22:35:25.000Z",
  "updated": "2020-05-09T22:35:25.000Z",
  "title": "The Bramson correction for Fisher--KPP equations with nonlocal diffusion",
  "authors": [
    "Cole Graham"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish the logarithmic Bramson correction to the position of solutions to the Fisher--KPP equation with nonlocal diffusion. Solutions with step-like initial data typically resemble a front at position $c_{*} t - \\frac{3}{2 \\lambda_{*}} \\log t + \\mathcal{O}(1)$ for explicit constants $c_{*}$ and $\\lambda_{*}$. However, certain singular diffusions exhibit more exotic behavior.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-09T22:35:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35K57",
      "60J80"
    ],
    "keywords": [
      "nonlocal diffusion",
      "fisher-kpp equation",
      "initial data typically resemble",
      "logarithmic bramson correction",
      "step-like initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}