{
  "id": "1804.02501",
  "version": "v1",
  "published": "2018-04-07T03:41:32.000Z",
  "updated": "2018-04-07T03:41:32.000Z",
  "title": "Chemotaxis effect vs logistic damping on boundedness in the 2-D minimal Keller-Segel model",
  "authors": [
    "Hai-Yang Jin",
    "Tian Xiang"
  ],
  "comment": "13 pages, under review",
  "journal": "2018, Comptes Rendus de l Acad\\'emie des Sciences - Series I - Mathematics",
  "doi": "10.1016/j.crma.2018.07.002",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study chemotaxis effect vs logistic dampening on boundedness for the two-dimensional minimal Keller-Segel model with logistic source in a 2-D smooth and bounded domain. It is well-known that this model allows only for global and uniform-in-time bounded solutions for any chemotactic strength and logistic dampening. Here, we carefully employ a simple and new method to regain its boundedness and, with particular attention to how boundedness depends qualitatively on the coefficient of chemotactic strength and logistic dampening rate. Up to a scaling constant depending only on initial data and the domain, we provide explicit upper bounds for the the solution components of the corresponding initial-boundary value problem. This qualitative boundedness results seems to be the first result in the regard.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-07T03:41:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K51"
    ],
    "keywords": [
      "boundedness",
      "logistic damping",
      "logistic dampening",
      "two-dimensional minimal keller-segel model",
      "chemotactic strength"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}