{
  "id": "1903.06448",
  "version": "v1",
  "published": "2019-03-15T10:37:25.000Z",
  "updated": "2019-03-15T10:37:25.000Z",
  "title": "Initial Data Identification in Conservation Laws and Hamilton-Jacobi Equations",
  "authors": [
    "Rinaldo Colombo",
    "Vincent Perrollaz"
  ],
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "In the scalar 1D case, conservation laws and Hamilton-Jacobi equations are deeply related. For both, we characterize those profiles that can be attained as solutions at a given positive time corresponding to at least one initial datum. Then, for each of the two equations, we precisely identify all those initial data yielding a solution that coincide with a given profile at that positive time. Various topological and geometrical properties of the set of these initial data are then proved. 2000 Mathematics Subject Classification: 35L65, 35F21, 93B30, 35R30.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-15T10:37:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "initial datum",
      "initial data identification",
      "conservation laws",
      "hamilton-jacobi equations",
      "positive time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}