{
  "id": "2007.04588",
  "version": "v1",
  "published": "2020-07-09T06:55:59.000Z",
  "updated": "2020-07-09T06:55:59.000Z",
  "title": "Blow up for a nonlinear PDE",
  "authors": [
    "Diego Chamorro",
    "Elena Issoglio"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a parabolic-type PDE with a diffusion given by a fractional Laplacian operator and with a quadratic nonlinearity of the 'gradient' of the solution, convoluted with a singular term b. Our first result is the well-posedness for this problem: We show existence and uniqueness of a (local in time) mild solution. The main result is about blow-up of said solution, and in particular we find sufficient conditions on the initial datum and on the term b to ensure blow-up of the solution in finite time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-09T06:55:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear pde",
      "fractional laplacian operator",
      "initial datum",
      "sufficient conditions",
      "finite time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}