{
  "id": "1703.10662",
  "version": "v1",
  "published": "2017-03-30T20:21:47.000Z",
  "updated": "2017-03-30T20:21:47.000Z",
  "title": "The unsaturated flow in porous media with dynamic capillary pressure",
  "authors": [
    "Josipa-Pina Milišić"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we consider a degenerate pseudoparabolic equation for the wetting saturation of an unsaturated two-phase flow in porous media with dynamic capillary pressure-saturation relationship where the relaxation parameter depends on the saturation. Following the approach given in [12] the existence of a weak solution is proved using Galerkin approximation and regularization techniques. A priori estimates needed for passing to the limit when the regularization parameter goes to zero are obtained by using appropriate test-functions, motivated by the fact that considered PDE allows a natural generalization of the classical Kullback entropy. Finally, a special care was given in obtaining an estimate of the mixed third-order term by combining the information from the capillary pressure with obtained a priori estimates on the saturation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-30T20:21:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K65",
      "35K70",
      "35Q35",
      "76S05"
    ],
    "keywords": [
      "porous media",
      "unsaturated flow",
      "priori estimates",
      "dynamic capillary pressure-saturation relationship",
      "degenerate pseudoparabolic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}