{
  "id": "1707.07456",
  "version": "v1",
  "published": "2017-07-24T09:50:34.000Z",
  "updated": "2017-07-24T09:50:34.000Z",
  "title": "Estimates of the Domain of Dependence for Scalar Conservation Laws",
  "authors": [
    "Nikolay Pogodaev"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Cauchy problem for a multidimensional scalar conservation law and construct an outer estimate for the domain of dependence of its Kruzkov solution. The estimate can be represented as the controllability set of a specific differential inclusion. In addition, reachable sets of this inclusion provide outer estimates for the support of the wave profiles. Both results follow from a modified version of the classical Kruzkov uniqueness theorem, which we also present in the paper. Finally, the results are applied to a control problem consisting in steering a distributed quantity to a given set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-24T09:50:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "93B03"
    ],
    "keywords": [
      "dependence",
      "multidimensional scalar conservation law",
      "outer estimate",
      "classical kruzkov uniqueness theorem",
      "specific differential inclusion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}