{
  "id": "1804.07624",
  "version": "v1",
  "published": "2018-04-20T14:02:37.000Z",
  "updated": "2018-04-20T14:02:37.000Z",
  "title": "Convex Integration for Diffusion Equations",
  "authors": [
    "Baisheng Yan"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the general diffusion equations with nonmonotone diffusion flux. We prove that certain geometric structures of a general nonmonotone flux function ensure the existence of infinitely many Lipschitz solutions to the diffusion equation. Relevant structures are characterized by certain bounded open sets satisfying the so-called chord condition and sufficient conditions for such sets are also given. Our method relies on a modification of the convex integration and Baire's category methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-20T14:02:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35M10",
      "35K55",
      "35D30",
      "49J45",
      "49K21"
    ],
    "keywords": [
      "convex integration",
      "general nonmonotone flux function ensure",
      "nonmonotone diffusion flux",
      "general diffusion equations",
      "baires category methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}