{
  "id": "2410.21123",
  "version": "v1",
  "published": "2024-10-28T15:27:45.000Z",
  "updated": "2024-10-28T15:27:45.000Z",
  "title": "Identification of source terms in the Schrödinger equation with dynamic boundary conditions from final data",
  "authors": [
    "Salah-Eddine Chorfi",
    "Alemdar Hasanov",
    "Roberto Morales"
  ],
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "In this paper, we study an inverse problem of identifying two spatial-temporal source terms in the Schr\\\"odinger equation with dynamic boundary conditions from the final time overdetermination. We adopt a weak solution approach to solve the inverse source problem. By analyzing the associated Tikhonov functional, we prove a gradient formula of the functional in terms of the solution to a suitable adjoint system, allowing us to obtain the Lipschitz continuity of the gradient. Next, the existence and uniqueness of a quasi-solution are also investigated. Finally, our theoretical results are validated by numerical experiments in one dimension using the Landweber iteration method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-28T15:27:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10",
      "35R25",
      "35R30",
      "49N45",
      "47A05"
    ],
    "keywords": [
      "dynamic boundary conditions",
      "schrödinger equation",
      "final data",
      "identification",
      "spatial-temporal source terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}