{
  "id": "2103.02241",
  "version": "v1",
  "published": "2021-03-03T08:07:15.000Z",
  "updated": "2021-03-03T08:07:15.000Z",
  "title": "Remarks on finite-time blow-up in a fully parabolic attraction-repulsion chemotaxis system via reduction to the Keller-Segel system",
  "authors": [
    "Yutaro Chiyo",
    "Tomomi Yokota"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper deals with the fully parabolic attraction-repulsion chemotaxis system, \\begin{align*} u_t=\\Delta u-\\chi\\nabla \\cdot (u\\nabla v)+\\xi \\nabla\\cdot(u \\nabla w), \\quad v_t=\\Delta v-v+u, \\quad w_t=\\Delta w-w+u, \\quad x \\in \\Omega,\\ t>0 \\end{align*} under homogeneous Neumann boundary conditions and initial conditions, where $\\Omega$ is an open ball in $\\mathbb{R}^n$ ($n \\ge 3$), $\\chi, \\xi>0$ are constants. When $w=0$, finite-time blow-up in the corresponding Keller-Segel system has already been obtained. However, finite-time blow-up in the above attraction-repulsion chemotaxis system has not yet been established. This paper provides an answer to this open problem by using a transformation with the structural advantage of the system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-03T08:07:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B44",
      "35Q92",
      "92C17"
    ],
    "keywords": [
      "fully parabolic attraction-repulsion chemotaxis system",
      "finite-time blow-up",
      "keller-segel system",
      "homogeneous neumann boundary conditions",
      "paper deals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}