{
  "id": "1008.0262",
  "version": "v2",
  "published": "2010-08-02T09:32:47.000Z",
  "updated": "2011-06-24T12:16:03.000Z",
  "title": "Gradient Systems on Networks",
  "authors": [
    "Delio Mugnolo",
    "René Pröpper"
  ],
  "comment": "11 pages, revised version",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a class of linear differential operators acting on vector-valued function spaces with general coupled boundary conditions. Unlike in the more usual case of so-called quantum graphs, the boundary conditions can be nonlinear. After introducing a suitable Lyapunov function we prove well-posedness and invariance results for the corresponding nonlinear diffusion problem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-24T12:16:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K51",
      "35R02",
      "47H20"
    ],
    "keywords": [
      "gradient systems",
      "general coupled boundary conditions",
      "corresponding nonlinear diffusion problem",
      "function spaces",
      "usual case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.0262M"
    }
  }
}