{
  "id": "1011.4488",
  "version": "v1",
  "published": "2010-11-19T18:22:44.000Z",
  "updated": "2010-11-19T18:22:44.000Z",
  "title": "A condition on delay for differential equations with discrete state-dependent delay",
  "authors": [
    "A. V. Rezounenko"
  ],
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "Parabolic differential equations with discrete state-dependent delay are studied. The approach, based on an additional condition on the delay function introduced in [A.V. Rezounenko, Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions, Nonlinear Analysis: Theory, Methods and Applications, 70 (11) (2009), 3978-3986] is developed. We propose and study a state-dependent analogue of the condition which is sufficient for the well-posedness of the corresponding initial value problem on the whole space of continuous functions $C$. The dynamical system is constructed in $C$ and the existence of a compact global attractor is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-19T18:22:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R10",
      "35B41",
      "35K57"
    ],
    "keywords": [
      "discrete state-dependent delay",
      "compact global attractor",
      "continuous functions",
      "corresponding initial value problem",
      "parabolic differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.4488R"
    }
  }
}