{
  "id": "2401.06928",
  "version": "v1",
  "published": "2024-01-12T23:29:11.000Z",
  "updated": "2024-01-12T23:29:11.000Z",
  "title": "Approximate solutions for the Vlasov--Poisson system with boundary layers",
  "authors": [
    "Chang-Yeol Jung",
    "Bongsuk Kwon",
    "Masahiro Suzuki",
    "Masahiro Takayama"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We construct the approximate solutions to the Vlasov--Poisson system in a half-space, which arises in the study of the quasi-neutral limit problem in the presence of a sharp boundary layer, referred as to the plasma sheath in the context of plasma physics. The quasi-neutrality is an important characteristic of plasmas and its scale is characterized by a small parameter, called the Debye length. We present the approximate equations obtained by a formal expansion in the parameter and study the properties of the approximate solutions. Moreover, we present numerical experiments demonstrating that the approximate solutions converge to those of the Vlasov--Poisson system as the parameter goes to zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-12T23:29:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vlasov-poisson system",
      "quasi-neutral limit problem",
      "sharp boundary layer",
      "approximate solutions converge",
      "plasma physics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}