{
  "id": "1608.07991",
  "version": "v1",
  "published": "2016-08-29T10:52:40.000Z",
  "updated": "2016-08-29T10:52:40.000Z",
  "title": "Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption",
  "authors": [
    "Johannes Lankeit",
    "Yulan Wang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system \\begin{eqnarray*} \\begin{array}{llc} u_t=\\Delta u-\\chi\\nabla\\cdot (u\\nabla v)+\\kappa u-\\mu u^2,\\\\ v_t=\\Delta v-uv, \\end{array} \\end{eqnarray*} in $N$-dimensional bounded smooth domains for suitably regular positive initial data. We shall establish the existence of a global bounded classical solution for suitably large $\\mu$ and prove that for any $\\mu>0$ there exists a weak solution. Moreover, in the case of $\\kappa>0$ convergence to the constant equilibrium $(\\frac{\\kappa}{\\mu},0)$ is shown.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-29T10:52:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q92",
      "35K55",
      "35A01",
      "35B40",
      "35D30",
      "92C17"
    ],
    "keywords": [
      "high-dimensional chemotaxis system",
      "global existence",
      "consumption",
      "boundedness",
      "stabilization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}