{
  "id": "1602.07262",
  "version": "v1",
  "published": "2016-02-23T18:45:59.000Z",
  "updated": "2016-02-23T18:45:59.000Z",
  "title": "Intermittency fronts for space-time fractional stochastic partial differential equations in $(d+1)$ dimensions",
  "authors": [
    "Sunday A. Asogwa",
    "Erkan Nane"
  ],
  "comment": "17 pages, submitted for publication. arXiv admin note: substantial text overlap with arXiv:1409.7468",
  "categories": [
    "math.PR",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We consider time fractional stochastic heat type equation $$\\partial^\\beta_tu_t(x)=-\\nu(-\\Delta)^{\\alpha/2} u_t(x)+I^{1-\\beta}_t[\\sigma(u)\\stackrel{\\cdot}{W}(t,x)]$$ in $(d+1)$ dimensions, where $\\nu>0$, $\\beta\\in (0,1)$, $\\alpha\\in (0,2]$, $d<\\min\\{2,\\beta^{-1}\\}\\a$, $\\partial^\\beta_t$ is the Caputo fractional derivative, $-(-\\Delta)^{\\alpha/2} $ is the generator of an isotropic stable process, $\\stackrel{\\cdot}{W}(t,x)$ is space-time white noise, and $\\sigma:\\R \\to\\RR{R}$ is Lipschitz continuous. Mijena and Nane proved in \\cite{JebesaAndNane1} that : (i) absolute moments of the solutions of this equation grows exponentially; and (ii) the distances to the origin of the farthest high peaks of those moments grow exactly linearly with time. The last result was proved under the assumptions $\\alpha=2$ and $d=1.$ In this paper we extend this result to the case $\\alpha=2$ and $d\\in\\{1,2,3\\}.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-23T18:45:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15"
    ],
    "keywords": [
      "space-time fractional stochastic partial differential",
      "fractional stochastic partial differential equations",
      "intermittency fronts",
      "fractional stochastic heat type",
      "stochastic heat type equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160207262A"
    }
  }
}