{
  "id": "0808.0250",
  "version": "v1",
  "published": "2008-08-02T11:19:47.000Z",
  "updated": "2008-08-02T11:19:47.000Z",
  "title": "Contraction in $L^1$ and large time behavior for a system arising in chemical reactions and molecular motors",
  "authors": [
    "M. Chipot",
    "D. Hilhorst",
    "D. Kinderlehrer",
    "M. Olech"
  ],
  "comment": "20 pages, packages used: amsmath, amssymb, amsthm, mathrsfs, bbm, nicefrac",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a contraction in $L^1$ property for the solutions of a nonlinear reaction--diffusion system whose special cases include intercellular transport as well as reversible chemical reactions. Assuming the existence of stationary solutions we show that the solutions stabilize as $t$ tends to infinity. Moreover, in the special case of linear reaction terms, we prove the existence and the uniqueness (up to a multiplicative constant) of the stationary solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-02T11:19:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34D23",
      "35K45",
      "35K50",
      "35K55",
      "35K57",
      "92C37",
      "92C45"
    ],
    "keywords": [
      "large time behavior",
      "chemical reactions",
      "molecular motors",
      "system arising",
      "contraction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.0250C"
    }
  }
}