{
  "id": "2007.15856",
  "version": "v1",
  "published": "2020-07-31T05:39:41.000Z",
  "updated": "2020-07-31T05:39:41.000Z",
  "title": "Discontinuous solutions of Hamilton-Jacobi equations versus Radon measure-valued solutions of scalar conservation laws: Disappearance of singularities",
  "authors": [
    "M. Bertsch",
    "F. Smarrazzo",
    "A. Terracina",
    "A. Tesei"
  ],
  "comment": "33 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $H$ be a bounded and Lipschitz continuous function. We consider discontinuous viscosity solutions of the Hamilton-Jacobi equation $U_{t}+H(U_x)=0$ and signed Radon measure valued entropy solutions of the conservation law $u_{t}+[H(u)]_x=0$. After having proved a precise statement of the formal relation $U_x=u$, we establish estimates for the (strictly positive!) times at which singularities of the solutions disappear. Here singularities are jump discontinuities in case of the Hamilton-Jacobi equation and signed singular measures in case of the conservation law.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-31T05:39:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scalar conservation laws",
      "hamilton-jacobi equation",
      "radon measure-valued solutions",
      "discontinuous solutions",
      "singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}