{
  "id": "1112.0415",
  "version": "v4",
  "published": "2011-12-02T10:09:42.000Z",
  "updated": "2014-01-03T21:37:16.000Z",
  "title": "Well-posedness and spectral properties of heat and wave equations with non-local conditions",
  "authors": [
    "Delio Mugnolo",
    "Serge Nicaise"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We consider the one-dimensional heat and wave equations but -- instead of boundary conditions-- we impose on the solution certain non-local, integral constraints. An appropriate Hilbert setting leads to an integration-by-parts formula in Sobolev spaces of negative order and eventually allows us to use semigroup theory leading to analytic well-posedness, hence sharpening regularity results previously obtained by other authors. In doing so we introduce a parametrization of such integral conditions that includes known cases but also shows the connection with more usual boundary conditions, like periodic ones. In the self-adjoint case, we even obtain eigenvalue asymptotics of so-called Weyl's type.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-01-03T21:37:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D06",
      "35J20",
      "34B10"
    ],
    "keywords": [
      "wave equations",
      "spectral properties",
      "non-local conditions",
      "usual boundary conditions",
      "integral constraints"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.0415M"
    }
  }
}