{
  "id": "2211.05814",
  "version": "v1",
  "published": "2022-11-10T19:12:12.000Z",
  "updated": "2022-11-10T19:12:12.000Z",
  "title": "Synchronisation for scalar conservation laws via Dirichlet boundary",
  "authors": [
    "Ana Djurdjevac",
    "Tommaso Rosati"
  ],
  "comment": "21 pages. Comments welcome",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We provide an elementary proof of geometric synchronisation for scalar conservation laws on a domain with Dirichlet boundary conditions. Unlike previous results, our proof does not rely on a strict maximum principle, and builds instead on a quantitative estimate of the dissipation at the boundary. We identify a coercivity condition under which the estimates are uniform over all initial conditions, via the construction of suitable super- and sub-solutions. In lack of such coercivity our results build on Lp energy estimates and a Lyapunov structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-10T19:12:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "37H15",
      "37L55",
      "37A25"
    ],
    "keywords": [
      "scalar conservation laws",
      "synchronisation",
      "dirichlet boundary conditions",
      "strict maximum principle",
      "lp energy estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}