{
  "id": "1603.01676",
  "version": "v1",
  "published": "2016-03-05T03:44:46.000Z",
  "updated": "2016-03-05T03:44:46.000Z",
  "title": "Explosive solutions of parabolic stochastic partial differential equations with L$\\acute{e}$vy noise",
  "authors": [
    "Kexue Li",
    "Jigen Peng",
    "Junxiong Jia"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study the explosive solutions to a class of parbolic stochastic semilinear differential equations driven by a L$\\acute{\\mbox{e}}$vy type noise. The sufficient conditions are presented to guarantee the existence of a unique positive solution of the stochastic partial differential equation under investigation. Moreover, we show that the positive solutions will blow up in finite time in mean $L^{p}$-norm sense, provided that the initial data, the nonlinear term and the multiplicative noise satisfies some conditions. Several examples are presented to illustrated the theory. Finally, we establish a global existence theorem based on a Lyapunov functional and prove that a stochastic Allen-Cahn equation driven by L$\\acute{\\mbox{e}}$vy noise has a global solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-05T03:44:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60J75"
    ],
    "keywords": [
      "parabolic stochastic partial differential equations",
      "vy noise",
      "explosive solutions",
      "stochastic semilinear differential equations",
      "semilinear differential equations driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}