{
  "id": "1310.5253",
  "version": "v2",
  "published": "2013-10-19T17:28:48.000Z",
  "updated": "2013-12-05T07:36:37.000Z",
  "title": "Stability properties for quasilinear parabolic equations with measure data and applications",
  "authors": [
    "Marie-Françoise Bidaut-Véron",
    "Hung Nguyen Quoc"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Omega$ be a bounded domain of $\\mathbb{R}^{N}$, and $Q=\\Omega \\times(0,T).$ We first study the problem \\[ \\left\\{ \\begin{array} [c]{l}% {u_{t}}-{\\Delta_{p}}u=\\mu\\qquad\\text{in }Q,\\\\ {u}=0\\qquad\\text{on }\\partial\\Omega\\times(0,T),\\\\ u(0)=u_{0}\\qquad\\text{in }\\Omega, \\end{array} \\right. \\] where $p>1$, $\\mu\\in\\mathcal{M}_{b}(\\Omega)$ and $u_{0}\\in L^{1}(\\Omega).$ Our main result is a \\textit{stability theorem }extending the results of Dal Maso, Murat, Orsina, Prignet, for the elliptic case\\textit{. } As an application, we consider the perturbed problem\\textit{ } \\[ \\left\\{ \\begin{array} [c]{l}% {u_{t}}-{\\Delta_{p}}u+\\mathcal{G}(u)=\\mu\\qquad\\text{in }Q,\\\\ {u}=0\\qquad\\text{on }\\partial\\Omega\\times(0,T),\\\\ u(0)=u_{0}\\qquad\\text{in }\\Omega, \\end{array} \\right. \\] where $\\mathcal{G}(u)$ may be an absorption or a source term$.$ In the model case $\\mathcal{G}(u)=\\pm\\left\\vert u\\right\\vert ^{q-1}u$ $(q>p-1),$ or $\\mathcal{G}$ has an exponential type. We give existence results when $q$ is subcritical, or when the measure $\\mu$ is good in time and satisfies suitable capacity conditions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-05T07:36:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasilinear parabolic equations",
      "measure data",
      "stability properties",
      "application",
      "satisfies suitable capacity conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.5253B"
    }
  }
}