{
  "id": "2211.14735",
  "version": "v1",
  "published": "2022-11-27T05:53:52.000Z",
  "updated": "2022-11-27T05:53:52.000Z",
  "title": "Entropy solutions to the Dirichlet problem for nonlinear diffusion equations with conservative noise",
  "authors": [
    "Kai Du",
    "Ruoyang Liu",
    "Yuxing Wang"
  ],
  "comment": "33 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "Motivated by porous medium equations with randomly perturbed velocity field, this paper considers a class of nonlinear degenerate diffusion equations with nonlinear conservative noise in bounded domains. The existence, uniqueness and $L_{1}$-stability of non-negative entropy solutions under the homogeneous Dirichlet boundary condition are proved. The approach combines Kruzhkov's doubling variables technique with a revised strong entropy condition that is automatically satisfied by the solutions of approximate equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-27T05:53:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60",
      "35K59"
    ],
    "keywords": [
      "nonlinear diffusion equations",
      "entropy solutions",
      "conservative noise",
      "dirichlet problem",
      "nonlinear degenerate diffusion equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}