{
  "id": "1504.01907",
  "version": "v1",
  "published": "2015-04-08T10:47:06.000Z",
  "updated": "2015-04-08T10:47:06.000Z",
  "title": "Rigorous Estimates on Balance Laws in Bounded Domains",
  "authors": [
    "Rinaldo M. Colombo",
    "Elena Rossi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in Bardos, Leroux and N\\'ed\\'elec (1979), striving to provide a rigorous treatment and detailed references.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-08T10:47:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L50",
      "35L65"
    ],
    "keywords": [
      "bounded domain",
      "rigorous estimates",
      "initial-boundary value problem",
      "general balance law",
      "entropy solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150401907C"
    }
  }
}