{
  "id": "1408.0815",
  "version": "v1",
  "published": "2014-08-04T20:50:30.000Z",
  "updated": "2014-08-04T20:50:30.000Z",
  "title": "Relative entropy in hyperbolic relaxation for balance laws",
  "authors": [
    "Alexey Miroshnikov",
    "Konstantina Trivisa"
  ],
  "journal": "Communications in Mathematical Sciences, Vol. 12, No. 6, pp. 1017-1043, 2014",
  "doi": "10.4310/CMS.2014.v12.n6.a2",
  "categories": [
    "math.AP"
  ],
  "abstract": "We present a general framework for the approximation of systems of hyperbolic balance laws. The novelty of the analysis lies in the construction of suitable relaxation systems and the derivation of a delicate estimate on the relative entropy. We provide a direct proof of convergence in the smooth regime for a wide class of physical systems. We present results for systems arising in materials science, where the presence of source terms presents a number of additional challenges and requires delicate treatment. Our analysis is in the spirit of the framework introduced by Tzavaras [A. Tzavaras, Commun. Math. Sci., 3-2, 2005] for systems of hyperbolic conservation laws.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-04T20:50:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B35",
      "76N10"
    ],
    "keywords": [
      "relative entropy",
      "hyperbolic relaxation",
      "hyperbolic conservation laws",
      "hyperbolic balance laws",
      "general framework"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.0815M"
    }
  }
}