{
  "id": "2311.02507",
  "version": "v1",
  "published": "2023-11-04T20:54:04.000Z",
  "updated": "2023-11-04T20:54:04.000Z",
  "title": "Linear orbital stability of discrete shock profiles for systems of conservation laws",
  "authors": [
    "Lucas Coeuret"
  ],
  "comment": "75 pages",
  "categories": [
    "math.NA",
    "cs.NA",
    "math.AP"
  ],
  "abstract": "We prove the linear orbital stability of spectrally stable stationary discrete shock profiles for conservative finite difference schemes applied to systems of conservation laws. The proof relies on a precise description of the pointwise asymptotic behavior of the Green's function associated with those discrete shock profiles, improving on the result of Godillon [God03]. The main novelty of this stability result is that it applies for a fairly large family of schemes that introduce some artificial viscosity and most importantly, that we do not impose any weakness assumption on the shock.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-04T20:54:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "65M06"
    ],
    "keywords": [
      "linear orbital stability",
      "conservation laws",
      "finite difference schemes",
      "stable stationary discrete shock profiles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 75,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}