{
  "id": "math/0603656",
  "version": "v1",
  "published": "2006-03-28T14:58:22.000Z",
  "updated": "2006-03-28T14:58:22.000Z",
  "title": "Global existence versus blow up for some models of interacting particles",
  "authors": [
    "Piotr Biler",
    "Lorenzo Brandolese"
  ],
  "comment": "Colloq. Math. (to appear)",
  "journal": "Colloq. Math. 106, 2 (2006) 293--303",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and the Debye-Hukel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method by S. Montgomery-Smith.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-28T14:58:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "92C17",
      "35Q60"
    ],
    "keywords": [
      "global existence",
      "interacting particles",
      "nonlocal parabolic semilinear equations",
      "debye-hukel drift-diffusion systems",
      "finite time blow"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3656B"
    }
  }
}