{
  "id": "1011.2444",
  "version": "v1",
  "published": "2010-11-10T17:49:16.000Z",
  "updated": "2010-11-10T17:49:16.000Z",
  "title": "Non-local PDEs with discrete state-dependent delays: well-posedness in a metric space",
  "authors": [
    "Alexander V. Rezounenko",
    "Petr Zagalak"
  ],
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of continuously differentiable (with respect to an appropriate norm) functions is used to construct a dynamical system. This subset is an analogue of \\textit{the solution manifold} proposed for ordinary equations in [H.-O. Walther, The solution manifold and $C\\sp 1$-smoothness for differential equations with state-dependent delay, J. Differential Equations, {195}(1), (2003) 46--65]. The existence of a compact global attractor is proven.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-10T17:49:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R10",
      "35B41",
      "35K57"
    ],
    "keywords": [
      "discrete state-dependent delays",
      "metric space",
      "non-local pdes",
      "well-posedness",
      "solution manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.2444R"
    }
  }
}