{
  "id": "1405.2223",
  "version": "v1",
  "published": "2014-05-09T13:22:48.000Z",
  "updated": "2014-05-09T13:22:48.000Z",
  "title": "Relative entropy in multi-phase models of 1d elastodynamics: Convergence of a non-local to a local model",
  "authors": [
    "Jan Giesselmann"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model converge to those of the local model in a certain regime. The arguments are based on the relative entropy framework and provide an example how local and non-local regularizations may compensate for non-convexity of the energy and enable the use of the relative entropy stability theory -- even if the energy is not quasi- or poly-convex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-09T13:22:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "35Q74",
      "82B26",
      "74N20"
    ],
    "keywords": [
      "multi-phase models",
      "1d elastodynamics",
      "non-local regularization",
      "convergence",
      "relative entropy stability theory"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2015.01.047",
      "journal": "Journal of Differential Equations",
      "year": 2015,
      "month": "May",
      "volume": 258,
      "number": 10,
      "pages": 3589
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JDE...258.3589G"
    }
  }
}