{
  "id": "1003.4182",
  "version": "v1",
  "published": "2010-03-22T14:58:55.000Z",
  "updated": "2010-03-22T14:58:55.000Z",
  "title": "Blow-up, concentration phenomenon and global existence for the Keller-Segel model in high dimension",
  "authors": [
    "Vincent Calvez",
    "Lucilla Corrias",
    "Mohammed Abderrahman Ebde"
  ],
  "comment": "44 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is devoted to the analysis of the classical Keller-Segel system over $\\mathbb{R}^d$, $d\\geq 3$. We describe as much as possible the dynamics of the system characterized by various criteria, both in the parabolic-elliptic case and in the fully parabolic case. The main results when dealing with the parabolic-elliptic case are: local existence without smallness assumption on the initial density, global existence under an improved smallness condition and comparison of blow-up criteria. A new concentration phenomenon criteria for the fully parabolic case is also given. The analysis is completed by a visualization tool based on the reduction of the parabolic-elliptic system to a finite-dimensional dynamical system of gradient flow type, sharing features similar to the infinite-dimensional system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-22T14:58:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global existence",
      "keller-segel model",
      "high dimension",
      "fully parabolic case",
      "parabolic-elliptic case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.4182C"
    }
  }
}