{
  "id": "2307.06347",
  "version": "v1",
  "published": "2023-07-12T17:31:07.000Z",
  "updated": "2023-07-12T17:31:07.000Z",
  "title": "Lagrange's discrete model of the wave equation in dimension greater than one",
  "authors": [
    "Massimo Villarini"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "A celebrated theorem of Lagrange states that a solution of the wave equation with one-dimensional space variable is the uniform limit, as N tends to infinity, of a second order ODE obtained from a mechanical model discretizing a string as N identical harmonic oscillators. Answering to a question posed by G. Gallavotti we generalize this result to the case of any space dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-12T17:31:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lagranges discrete model",
      "wave equation",
      "dimension greater",
      "second order ode",
      "space dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}