{
  "id": "1312.2509",
  "version": "v1",
  "published": "2013-12-09T16:47:18.000Z",
  "updated": "2013-12-09T16:47:18.000Z",
  "title": "Parabolic equations with exponential nonlinearity and measure data",
  "authors": [
    "Phuoc-Tai Nguyen"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Omega$ be a bounded domain in ${\\mathbb R}^N$ and $T>0$. We study the problem \\begin{equation} (P)\\left\\{ \\begin{array}{lll} u_t - \\Delta u \\pm g(u) &= \\mu \\quad &\\text{in } Q_T:=\\Omega \\times (0,T) \\\\ \\phantom{------,} u&=0 &\\text{on } \\partial \\Omega \\times (0,T)\\\\ \\phantom{----,} u(.,0) &=\\omega &\\text{in } \\Omega. \\end{array} \\right. \\end{equation} where $\\mu$ and $\\omega$ are bounded Radon measures in $Q_T$ and $\\Omega$ respectively and $g(u) \\sim e^{a |u|^q} $ with $a>0$ and $q \\geq 1$. We provide a sufficient condition in terms of fractional maximal potentials of $\\mu$ and $\\omega$ for solving (P).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-09T16:47:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential nonlinearity",
      "measure data",
      "parabolic equations",
      "fractional maximal potentials",
      "bounded radon measures"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2014.05.051",
      "journal": "Journal of Differential Equations",
      "year": 2014,
      "month": "Oct",
      "volume": 257,
      "number": 7,
      "pages": 2704
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JDE...257.2704N"
    }
  }
}