{
  "id": "1701.00719",
  "version": "v1",
  "published": "2017-01-02T18:12:42.000Z",
  "updated": "2017-01-02T18:12:42.000Z",
  "title": "Comparision of the definitions of generalized solution of the Cauchy problem for quasi-linear equation",
  "authors": [
    "Alexander Gasnikov"
  ],
  "comment": "Preprint CCAS RAS, 2006 (3-d edition, 2016); 75 pages, in Russian",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In preprint we consider and compare different definitions of generalized solution of the Cauchy problem for 1d-scalar quasilinear equation (conservation law). We start from the classical approaches goes back to I.M. Gelfand, O.A. Oleinik, S.N. Kruzhkov and move to the modern finite-difference approximations approaches belongs to A.A. Shananin and G.M. Henkin. We discuss the conditions that provide definitions to be equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-02T18:12:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cauchy problem",
      "generalized solution",
      "quasi-linear equation",
      "definitions",
      "modern finite-difference approximations approaches belongs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 75,
      "language": "ru",
      "license": "arXiv",
      "status": "editable"
    }
  }
}