{
  "id": "2403.08450",
  "version": "v1",
  "published": "2024-03-13T12:06:39.000Z",
  "updated": "2024-03-13T12:06:39.000Z",
  "title": "Increasing stability for inverse source problem with limited-aperture far field data at multi-frequencies",
  "authors": [
    "Ibtissem Ben Aïcha",
    "Guanghui Hu",
    "Suliang Si"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the increasing stability of an inverse source problem for the Helmholtz equation from limited-aperture far field data at multiple wave numbers. The measurement data are givenby the far field patterns $u^\\infity(\\hat{x},k)$ for all observation directions in some neighborhood of a fixed direction $\\hat{x}$ and for all wave numbers k belonging to a finite interval $(0,K)$. In this paper, we discuss the increasing stability with respect to the width of the wavenumber interval $K>1$. In three dimensions we establish stability estimates of the $L^2$-norm and $H^{-1}$-norm of the source function from the far field data. The ill-posedness of the inverse source problem turns out to be of H\\\"older type while increasing the wavenumber band K. We also discuss an analytic continuation argument of the far-field data with respect to the wavenumbers at a fixed direction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-13T12:06:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "78A46"
    ],
    "keywords": [
      "limited-aperture far field data",
      "increasing stability",
      "inverse source problem turns",
      "multi-frequencies",
      "analytic continuation argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}