| Abstract: |
| This talk concerns cavity problems for the biharmonic equation in an unbounded Kirchhoff--Love plate. By applying a concentrated point force inside the plate and using two sets of boundary measurements, we address the inverse problem of determining an unknown cavity. A key component of the analysis is the construction of a Dirichlet-to-Neumann (DtN) map, which reduces the unbounded domain problem to an equivalent formulation on a bounded domain. This reduction enables a variational analysis and establishes the well-posedness of the direct problem and the uniqueness in recovering both the location and shape of the cavity by using of a unique continuation principle. |
|