{
  "id": "math/0602010",
  "version": "v1",
  "published": "2006-02-01T10:58:42.000Z",
  "updated": "2006-02-01T10:58:42.000Z",
  "title": "Global existence and causality for a transmission problem with a repulsive nonlinearity",
  "authors": [
    "F. Ali Mehmeti",
    "V. Regnier"
  ],
  "comment": "23 pages, no figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "It is well-known that the solution of the classical linear wave equation with compactly supported initial condition and vanishing initial velocity is also compactly supported in a set depending on time : the support of the solution at time t is causally related to that of the initially given condition. Reed and Simon have shown that for a real-valued Klein-Gordon equation with (nonlinear) right-hand side $- \\lambda u^3$, causality still holds. We show the same property for a one-dimensional Klein-Gordon problem but with transmission and with a more general repulsive nonlinear right-hand side $F$. We also prove the global existence of a solution using the repulsiveness of $F$. In the particular case $F(u) = - \\lambda u^3$, the problem is a physical model for a quantum particle submitted to self-interaction and to a potential step.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-01T10:58:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A05",
      "35C15",
      "35E15",
      "35L70",
      "35L90",
      "42A38"
    ],
    "keywords": [
      "global existence",
      "transmission problem",
      "repulsive nonlinearity",
      "general repulsive nonlinear right-hand side",
      "classical linear wave equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2010M"
    }
  }
}