{
  "id": "1412.0219",
  "version": "v1",
  "published": "2014-11-30T14:18:56.000Z",
  "updated": "2014-11-30T14:18:56.000Z",
  "title": "Parabolic partial differential equations with discrete state-dependent delay: classical solutions and solution manifold",
  "authors": [
    "Tibor Krisztin",
    "Alexander Rezounenko"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Classical solutions to PDEs with discrete state-dependent delay are studied. We prove the well-posedness in a set $X_F$ which is an analogous to the solution manifold used for ordinary differential equations with state-dependent delay. We prove that the evolution operators are $C^1$-smooth on the solution manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-30T14:18:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R10",
      "93C23"
    ],
    "keywords": [
      "parabolic partial differential equations",
      "discrete state-dependent delay",
      "solution manifold",
      "classical solutions",
      "ordinary differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.0219K"
    }
  }
}