{
  "id": "1810.12239",
  "version": "v1",
  "published": "2018-10-29T16:33:37.000Z",
  "updated": "2018-10-29T16:33:37.000Z",
  "title": "On the long time behavior of a tumor growth model",
  "authors": [
    "Alain Miranville",
    "Elisabetta Rocca",
    "Giulio Schimperna"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the problem of the long time dynamics for a diffuse interface model for tumor growth. The model describes the growth of a tumor surrounded by host tissues in the presence of a nutrient and consists in a Cahn-Hilliard-type equation for the tumor phase coupled with a reaction-diffusion equation for the nutrient concentration. We prove that, under physically motivated assumptions on parameters and data, the corresponding initial-boundary value problem generates a dissipative dynamical system that admits the global attractor in a proper phase space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-29T16:33:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D30",
      "35K57",
      "35Q92",
      "35B41",
      "37L30",
      "92C17"
    ],
    "keywords": [
      "long time behavior",
      "tumor growth model",
      "corresponding initial-boundary value problem generates",
      "proper phase space",
      "diffuse interface model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}