{
  "id": "1402.2061",
  "version": "v1",
  "published": "2014-02-10T08:09:24.000Z",
  "updated": "2014-02-10T08:09:24.000Z",
  "title": "On a time and space discretized approximation of the Boltzmann equation in the whole space",
  "authors": [
    "C. P. Grünfeld",
    "D. Marinescu"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper, convergence results on the solutions of a time and space discrete model approximation of the Boltzmann equation for a gas of Maxwellian particles in a bounded domain, obtained by Babovsky and Illner [1989], are extended to approximate the solutions of the Boltzmann equation in the whole physical space. This is done for a class of particle interactions including Maxwell and soft cut-off potentials in the sense of Grad. The main result shows that the solutions of the discrete model converge in $\\mathbb{L}^1$ to the solutions of the Boltzmann equation, when the discretization parameters go simultaneously to zero. The convergence is uniform with respect to the discretization parameters. In addition, a sufficient condition for the implementation of the main result is provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-10T08:09:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A35",
      "65M12",
      "76P05"
    ],
    "keywords": [
      "boltzmann equation",
      "space discretized approximation",
      "discretization parameters",
      "main result",
      "space discrete model approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.2061G"
    }
  }
}