{
  "id": "2010.04659",
  "version": "v1",
  "published": "2020-10-09T16:05:11.000Z",
  "updated": "2020-10-09T16:05:11.000Z",
  "title": "On nonnegative solutions for the Functionalized Cahn-Hilliard equation with degenerate mobility",
  "authors": [
    "Shibin Dai",
    "Qiang Liu",
    "Toai Luong",
    "Keith Promislow"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The Functionalized Cahn-Hilliard equation has been proposed as a model for the interfacial energy of phase-separated mixtures of amphiphilic molecules. We study the existence of a nonnegative weak solutions of a gradient flow of the Functionalized Cahn-Hilliard equation subject to a degenerate mobility M(u) that is zero for u<=0. Assuming the initial data u0(x) is positive, we construct a weak solution as the limit of solutions corresponding to nondegenerate mobilities and verify that it satisfies an energy dissipation inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-09T16:05:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35G20",
      "35G31"
    ],
    "keywords": [
      "degenerate mobility",
      "nonnegative solutions",
      "energy dissipation inequality",
      "initial data u0",
      "functionalized cahn-hilliard equation subject"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}