{
  "id": "2104.00212",
  "version": "v1",
  "published": "2021-04-01T02:43:48.000Z",
  "updated": "2021-04-01T02:43:48.000Z",
  "title": "Blow-up phenomena in a parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with superlinear logistic degradation",
  "authors": [
    "Yutaro Chiyo",
    "Monica Marras",
    "Yuya Tanaka",
    "Tomomi Yokota"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with the attraction-repulsion chemotaxis system with superlinear logistic degradation, \\begin{align*} \\begin{cases} u_t = \\Delta u - \\chi \\nabla\\cdot(u \\nabla v) + \\xi \\nabla\\cdot (u \\nabla w) + \\lambda u - \\mu u^k, \\quad &x \\in \\Omega,\\ t>0,\\\\[1.05mm] 0= \\Delta v + \\alpha u - \\beta v, \\quad &x \\in \\Omega,\\ t>0,\\\\[1.05mm] 0= \\Delta w + \\gamma u - \\delta w, \\quad &x \\in \\Omega,\\ t>0, \\end{cases} \\end{align*} under homogeneous Neumann boundary conditions, in a ball $\\Omega \\subset \\mathbb{R}^n$ ($n \\ge 3$), with constant parameters $\\lambda \\in \\mathbb{R}$, $k>1$, $\\mu, \\chi, \\xi, \\alpha, \\beta, \\gamma, \\delta>0$. Blow-up phenomena in the system have been well investigated in the case $\\lambda=\\mu=0$, whereas the attraction-repulsion chemotaxis system with logistic degradation has been not studied. Under the condition that $k>1$ is close to $1$, this paper ensures a solution which blows up in $L^\\infty$-norm and $L^\\sigma$-norm with some $\\sigma>1$ for some nonnegative initial data. Moreover, a lower bound of blow-up time is derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-01T02:43:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B44",
      "35Q92",
      "92C17"
    ],
    "keywords": [
      "parabolic-elliptic-elliptic attraction-repulsion chemotaxis system",
      "superlinear logistic degradation",
      "blow-up phenomena",
      "homogeneous neumann boundary conditions",
      "paper ensures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}