{
  "id": "1709.06676",
  "version": "v1",
  "published": "2017-09-19T23:28:52.000Z",
  "updated": "2017-09-19T23:28:52.000Z",
  "title": "Evolution of Interfaces for the Nonlinear Double Degenerate Parabolic Equation of Turbulent Filtration with Absorption",
  "authors": [
    "Ugur G. Abdulla",
    "Jian Du",
    "Adam Prinkey",
    "Chloe Ondracek",
    "Suneil Parimoo"
  ],
  "comment": "29 pages, 12 fugures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the short-time asymptotic formula for the interfaces and local solutions near the interfaces for the nonlinear double degenerate reaction-diffusion equation of turbulent filtration with strong absorption \\[ u_t=\\Big(|(u^{m})_x|^{p-1}(u^{m})_x\\Big)_x-bu^{\\beta}, \\, mp>1, \\, \\beta >0. \\] Full classification is pursued in terms of the nonlinearity parameters $m, p,\\beta$ and asymptotics of the initial function near its support. Numerical analysis using a weighted essentially nonoscillatory (WENO) scheme with interface capturing is implemented, and comparison of numerical and analytical results is presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-19T23:28:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35K65",
      "65M06"
    ],
    "keywords": [
      "nonlinear double degenerate parabolic equation",
      "turbulent filtration",
      "absorption",
      "nonlinear double degenerate reaction-diffusion equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}