{
  "id": "2408.13869",
  "version": "v1",
  "published": "2024-08-25T15:39:08.000Z",
  "updated": "2024-08-25T15:39:08.000Z",
  "title": "Runge approximation and its applications to fractional Calderón's problem for some nonlocal wave equations",
  "authors": [
    "Yi-Hsuan Lin",
    "Teemu Tyni",
    "Philipp Zimmermann"
  ],
  "comment": "38 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The main purpose of this article is to establish the Runge-type approximation in $L^2(0,T;\\widetilde{H}^s(\\Omega))$ for solutions of linear nonlocal wave equations. To achieve this, we extend the theory of very weak solutions for classical wave equations to our nonlocal framework. This strengthened Runge approximation property allows us to extend the existing uniqueness results for Calder\\'on problems of linear and nonlinear nonlocal wave equations in our earlier works. Furthermore, we prove unique determination results for the Calder\\'on problem of nonlocal wave equations with polyhomogeneous nonlinearities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-25T15:39:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "26A33",
      "42B37"
    ],
    "keywords": [
      "fractional calderóns problem",
      "calderon problem",
      "applications",
      "nonlinear nonlocal wave equations",
      "unique determination results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}