{
  "id": "1709.07737",
  "version": "v1",
  "published": "2017-09-22T13:31:04.000Z",
  "updated": "2017-09-22T13:31:04.000Z",
  "title": "Global Stability for a Class of Nonlinear PDE with non-local term",
  "authors": [
    "Joseph G. Conlon",
    "Michael Dabkowski"
  ],
  "comment": "49 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE which have some similarity to the PDE of the Lifschitz-Slyozov-Wagner model. The method of proof does not involve a Lyapounov function. It is shown that stability for the PDE is equivalent to stability for a differential delay equation. Stability for the delay equation is proven by exploiting certain maximal properties. These are established by using the methods of optimal control theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-22T13:31:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35F20",
      "34K20",
      "49L20"
    ],
    "keywords": [
      "global stability",
      "nonlinear pde",
      "non-local term",
      "establishing global asymptotic stability results",
      "differential delay equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}