{
  "id": "2307.10887",
  "version": "v1",
  "published": "2023-07-20T14:06:00.000Z",
  "updated": "2023-07-20T14:06:00.000Z",
  "title": "Decay at infinity for solutions to some fractional parabolic equations",
  "authors": [
    "Agnid Banerjee",
    "Abhishek Ghosh"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2306.00341",
  "categories": [
    "math.AP"
  ],
  "abstract": "For $s \\in [1/2, 1)$, let $u$ solve $(\\partial_t - \\Delta)^s u = Vu$ in $\\mathbb R^{n} \\times [-T, 0]$ for some $T>0$ where $||V||_{ C^2(\\mathbb R^n \\times [-T, 0])} < \\infty$. We show that if for some $0< c< T$ and $\\epsilon>0$ $$\\frac{1}{c} \\int_{[-c,0]} u^2(x, t) dt \\leq Ce^{-|x|^{2+\\epsilon}}\\ \\forall x \\in \\mathbb R^n,$$ then $u \\equiv 0$ in $\\mathbb R^{n} \\times [-T, 0]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-20T14:06:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional parabolic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}