{
  "id": "2312.06373",
  "version": "v1",
  "published": "2023-12-11T13:31:12.000Z",
  "updated": "2023-12-11T13:31:12.000Z",
  "title": "Local controllability around a regular solution and null-controllability of scattering solutions for semilinear wave equations",
  "authors": [
    "Thomas Perrin"
  ],
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "On a Riemannian manifold of dimension $2 \\leq d \\leq 6$, with or without boundary, and whether bounded or unbounded, we consider a semilinear wave (or Klein-Gordon) equation with a subcritical nonlinearity, either defocusing or focusing. We establish local controllability around a partially analytic solution, under the geometric control condition. Specifically, some blow-up solutions can be controlled. In the case of a Klein-Gordon equation on a non-trapping exterior domain, we prove the null-controllability of scattering solutions. The proof is based on local energy decay and global-in-time Strichartz estimates. Some corollaries are given, including the null-controllability of a solution starting near the ground state in certain focusing cases, and exact controllability in certain defocusing cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-11T13:31:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semilinear wave equations",
      "scattering solutions",
      "regular solution",
      "null-controllability",
      "geometric control condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}