{
  "id": "1611.07282",
  "version": "v1",
  "published": "2016-11-22T12:53:52.000Z",
  "updated": "2016-11-22T12:53:52.000Z",
  "title": "Some non-existence results for a class of stochastic partial differential equations",
  "authors": [
    "Mohammud Foondun",
    "Wei Liu",
    "Erkan Nane"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider the following stochastic partial differential equation, \\begin{equation*} \\partial_t u_t(x)= \\mathcal{L}u_t(x)+ \\sigma (u_t(x))\\dot F(t,x)\\quad{t>0}\\quad\\text{and}\\quad x\\in R^d. \\end{equation*} The operator $\\mathcal{L}$ is the generator of a strictly stable process and $\\dot F$ is the random forcing term which is assumed to be Gaussian. Under some additional conditions, most notably on $\\sigma$ and the initial condition, we show non-existence of global random field solutions. Our results are new and complement earlier works.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-22T12:53:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H25"
    ],
    "keywords": [
      "stochastic partial differential equation",
      "non-existence results",
      "global random field solutions",
      "complement earlier works",
      "additional conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}