{
  "id": "1205.3651",
  "version": "v1",
  "published": "2012-05-16T12:21:13.000Z",
  "updated": "2012-05-16T12:21:13.000Z",
  "title": "Scalar conservation laws on constant and time-dependent Riemannian manifolds",
  "authors": [
    "Daniel Lengeler",
    "Thomas Müller"
  ],
  "comment": "23 pages, no figures",
  "doi": "10.1016/j.jde.2012.11.002",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we establish well-posedness for scalar conservation laws on closed manifolds M endowed with a constant or a time-dependent Riemannian metric for initial values in L^\\infty(M). In particular we show the existence and uniqueness of entropy solutions as well as the L^1 contraction property and a comparison principle for these solutions. Throughout the paper the flux function is allowed to depend on time and to have non-vanishing divergence. Furthermore, we derive estimates of the total variation of the solution for initial values in BV(M), and we give, in the case of a time-independent metric, a simple geometric characterisation of flux functions that give rise to total variation diminishing estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-16T12:21:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "58J45",
      "76N10"
    ],
    "keywords": [
      "scalar conservation laws",
      "time-dependent riemannian manifolds",
      "initial values",
      "flux function",
      "time-dependent riemannian metric"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Differential Equations",
      "year": 2013,
      "volume": 254,
      "number": 4,
      "pages": 1705
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JDE...254.1705L"
    }
  }
}