{
  "id": "1310.6633",
  "version": "v1",
  "published": "2013-10-24T14:31:21.000Z",
  "updated": "2013-10-24T14:31:21.000Z",
  "title": "Existence of mild solutions for a system of partial differential equations with time-dependent generators",
  "authors": [
    "Amanda del Carmen Andrade-González",
    "José Villa-Morales"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We give sufficient conditions for global existence of positive mild solutions for the weak coupled system: \\begin{eqnarray*} \\frac{\\partial u_{1}}{\\partial t} &=&\\rho_{1}t^{\\rho_{1}-1}\\Delta_{\\alpha_{1}}u_{1}+t^{\\sigma_{1}}u_{2}^{\\beta_{1}},\\ \\ u_{1}\\left(0\\right) =\\varphi_{1}, \\\\ \\frac{\\partial u_{2}}{\\partial t} &=&\\rho_{2}t^{\\rho_{2}-1}\\Delta_{\\alpha_{2}}u_{2}+t^{\\sigma_{2}}u_{1}^{\\beta_{2}},\\ \\ u_{2}\\left(0\\right) =\\varphi_{2}, \\end{eqnarray*} where $\\Delta_{\\alpha_{i}}$ is a fractional Laplacian, $0<\\alpha_{i}\\leq 2,\\ \\beta_{i}>1,\\ \\rho_{i}>0,\\ \\sigma_{i}>-1\\ $are constants and the initial data $\\varphi_{i}$ are positive, bounded and integrable functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-24T14:31:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35K45",
      "35B40",
      "35K20"
    ],
    "keywords": [
      "partial differential equations",
      "time-dependent generators",
      "sufficient conditions",
      "global existence",
      "positive mild solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6633A"
    }
  }
}