{
  "id": "0904.2473",
  "version": "v1",
  "published": "2009-04-16T12:02:03.000Z",
  "updated": "2009-04-16T12:02:03.000Z",
  "title": "Existence, positivity and stability for a nonlinear model of cellular proliferation",
  "authors": [
    "Mostafa Adimy",
    "Fabien Crauste"
  ],
  "journal": "Nonlinear Analysis Real World Applications 6, 2 (2005) 337-366",
  "doi": "10.1016/j.nonrwa.2004.09.001",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we investigate a system of two nonlinear partial differential equations, arising from a model of cellular proliferation which describes the production of blood cells in the bone marrow. Due to cellular replication, the two partial differential equations exhibit a retardation of the maturation variable and a temporal delay depending on this maturity. We show that this model has a unique solution which is global under a classical Lipschitz condition. We also obtain the positivity of the solutions and the local and global stability of the trivial equilibrium.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-16T12:02:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cellular proliferation",
      "nonlinear model",
      "positivity",
      "nonlinear partial differential equations",
      "global stability"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.2473A"
    }
  }
}