{
  "id": "2207.08516",
  "version": "v1",
  "published": "2022-07-18T11:21:10.000Z",
  "updated": "2022-07-18T11:21:10.000Z",
  "title": "Parabolic Differential Equations with Bounded Delay",
  "authors": [
    "Marek Kryspin",
    "Janusz Mierczyński"
  ],
  "comment": "40 pages",
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-* topology of delay coefficients is required. The results are important in the applications of the theory of Lyapunov exponents to the investigation of PDEs with delay.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-18T11:21:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35K15",
      "35R10"
    ],
    "keywords": [
      "parabolic differential equations",
      "bounded delay",
      "order parabolic partial differential equations",
      "second order parabolic partial differential",
      "linear nonautonomous second order parabolic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}