{
  "id": "math/0610808",
  "version": "v5",
  "published": "2006-10-26T18:53:14.000Z",
  "updated": "2009-01-24T16:22:31.000Z",
  "title": "A new approach to transport equations associated to a regular field: trace results and well-posedness",
  "authors": [
    "Luisa Arlotti",
    "Jacek Banasiak",
    "Bertrand Lods"
  ],
  "comment": "30 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We generalize known results on transport equations associated to a Lipschitz field $\\mathbf{F}$ on some subspace of $\\mathbb{R}^N$ endowed with some general space measure $\\mu$. We provide a new definition of both the transport operator and the trace measures over the incoming and outgoing parts of $\\partial \\Omega$ generalizing known results from the literature. We also prove the well-posedness of some suitable boundary-value transport problems and describe in full generality the generator of the transport semigroup with no-incoming boundary conditions.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2009-01-24T16:22:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D06",
      "47D05",
      "47N55",
      "35F05",
      "82C40"
    ],
    "keywords": [
      "transport equations",
      "regular field",
      "trace results",
      "well-posedness",
      "general space measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10808A"
    }
  }
}