{
  "id": "0811.0549",
  "version": "v1",
  "published": "2008-11-04T16:43:27.000Z",
  "updated": "2008-11-04T16:43:27.000Z",
  "title": "Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation",
  "authors": [
    "G. C. Coclite",
    "K. H. Karlsen",
    "Y. -S. Kwon"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary condition. Equipped with this formulation, we go on to establish the well-posedness of entropy solutions to the initial-boundary value problem. The proof utilizes the kinetic formulation and the compensated compactness method. Finally, we make use of these results to demonstrate the well-posedness in a class of discontinuous solutions to the initial-boundary value problem for the Degasperis-Procesi shallow water equation, which is a third order nonlinear dispersive equation that can be rewritten in the form of a nonlinear conservation law with a nonlocal source term.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-04T16:43:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "35G25"
    ],
    "keywords": [
      "initial-boundary value problem",
      "source term",
      "conservation law",
      "degasperis-procesi equation",
      "boundary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.0549C"
    }
  }
}