{
  "id": "2107.04459",
  "version": "v1",
  "published": "2021-07-09T14:24:30.000Z",
  "updated": "2021-07-09T14:24:30.000Z",
  "title": "Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity",
  "authors": [
    "Michael Salins"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "A condition is identified that implies that solutions to the stochastic reaction-diffusion equation $\\frac{\\partial u}{\\partial t} = \\mathcal{A} u + f(u) + \\sigma(u) \\dot{W}$ on a bounded spatial domain never explode. We consider the case where $\\sigma$ grows polynomially and $f$ is polynomially dissipative, meaning that $f$ strongly forces solutions toward finite values. This result demonstrates the role that the deterministic forcing term $f$ plays in preventing explosion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-09T14:24:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15"
    ],
    "keywords": [
      "stochastic reaction-diffusion equation",
      "super-linear multiplicative noise",
      "global solutions",
      "strong dissipativity",
      "deterministic forcing term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}