{
  "id": "1511.02510",
  "version": "v1",
  "published": "2015-11-08T17:48:19.000Z",
  "updated": "2015-11-08T17:48:19.000Z",
  "title": "Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems",
  "authors": [
    "Anna Marciniak-Czochra",
    "Grzegorz Karch",
    "Kanako Suzuki",
    "Jacek Zienkiewicz"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we provide an example of a class of two reaction-diffusion-ODE equations with homogeneous Neumann boundary conditions, in which Turing-type instability not only destabilizes constant steady states but also induces blow-up of nonnegative spatially heterogeneous solutions. Solutions of this problem preserve nonnegativity and uniform boundedness of the total mass. Moreover, for the corresponding system with two non-zero diffusion coefficients, all nonnegative solutions are global in time. We prove that a removal of diffusion in one of the equations leads to a finite-time blow-up of some nonnegative spatially heterogeneous solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-08T17:48:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonnegative solutions",
      "reaction-diffusion-ode systems",
      "diffusion-driven blowup",
      "nonnegative spatially heterogeneous solutions",
      "destabilizes constant steady states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151102510M"
    }
  }
}