{
  "id": "2407.18361",
  "version": "v1",
  "published": "2024-07-25T19:50:57.000Z",
  "updated": "2024-07-25T19:50:57.000Z",
  "title": "Inverse boundary value problem for the Convection-Diffusion equation with local data",
  "authors": [
    "Pranav Kumar",
    "Anamika Purohit"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a local data inverse problem for the time-dependent Convection-Diffusion Equation (CDE) in a bounded domain where a part of the boundary is treated to be inaccessible. Up on assuming the inaccessible part to be flat, we seek for the unique determination of the time-dependent convection and the density terms from the knowledge of the boundary data measured outside the inaccessible part. In the process, we show that there is a natural gauge in the perturbations, and we prove that this is the only obstruction in the uniqueness result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-25T19:50:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35K20"
    ],
    "keywords": [
      "inverse boundary value problem",
      "local data inverse problem",
      "inaccessible part",
      "boundary data measured outside",
      "time-dependent convection-diffusion equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}