{
  "id": "1805.09193",
  "version": "v1",
  "published": "2018-05-23T14:22:19.000Z",
  "updated": "2018-05-23T14:22:19.000Z",
  "title": "Global existence and boundedness of solutions to a chemotaxis-consumption model with singular sensitivity",
  "authors": [
    "Johannes Lankeit",
    "Giuseppe Viglialoro"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the zero-flux chemotaxis-system \\begin{equation*} \\begin{cases} u_t=\\Delta u -\\chi \\nabla \\cdot (\\frac{u}{v} \\nabla v) \\\\ v_t=\\Delta v-f(u)v \\end{cases} \\end{equation*} in a smooth and bounded domain $\\Omega$ of $\\mathbb{R}^2$, with $\\chi>0$ and $f\\in C^1(\\mathbb{R})$ essentially behaving like $u^\\beta$, $0<\\beta<1$. Precisely for $\\chi<1$ and any sufficiently regular initial data $u(x,0)\\geq 0$ and $v(x,0)>0$ on $\\bar{\\Omega}$, we show the existence of global classical solutions. Moreover, if additionally $m:=\\int_\\Omega u(x,0)$ is sufficiently small, then also their boundedness is achieved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-23T14:22:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q92",
      "35A01",
      "35K55",
      "35K51",
      "92C17"
    ],
    "keywords": [
      "global existence",
      "chemotaxis-consumption model",
      "singular sensitivity",
      "boundedness",
      "sufficiently regular initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}