{
  "id": "1904.04593",
  "version": "v1",
  "published": "2019-04-09T11:15:01.000Z",
  "updated": "2019-04-09T11:15:01.000Z",
  "title": "On the KPZ equation with fractional diffusion",
  "authors": [
    "Boumediene Abdellaoui",
    "Ireneo Peral",
    "Ana Primo"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "\\begin{abstract} In this work we analyze the existence of solution to the fractional quasilinear problem, $$ (P) \\left\\{ \\begin{array}{rcll} u_t+(-\\Delta )^s u &=&|\\nabla u|^{\\alpha}+ f &\\inn \\Omega_T\\equiv\\Omega\\times (0,T),\\\\ u(x,t)&=&0 & \\inn(\\mathbb{R}^N\\setminus\\Omega)\\times [0,T),\\\\ u(x,0)&=&u_{0}(x) & \\inn\\Omega,\\\\ \\end{array}\\right. $$ where $\\Omega$ is a $C^{1,1}$ bounded domain in $\\mathbb{R}^N$, $N> 2s$ and $\\frac{1}{2}<s<1$. We suppose that $f$ and $u_0$ are non negative functions satisfying some hypotheses that we will precise later. According to the value of $\\a$ and the regularity of $f$, we will show the existence of a solution to problem $(P)$. \\end{abstract}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-09T11:15:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K59",
      "47G20",
      "47J35"
    ],
    "keywords": [
      "fractional diffusion",
      "kpz equation",
      "fractional quasilinear problem",
      "non negative functions satisfying",
      "bounded domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}