Shitao Liu, University of Virginia


Inverse Problem for a Structural Acoustic Interaction Model

Abstract: Inverse problem of determining the potential caused by the source term entering an acoustic chamber is considered. The PDE model consists of wave equation coupled to plate equation with the coupling occurring at the interface--manifold of lower dimension. The source is being reconstructed from the measurements of acceleration of the elastic wall, which was modeled by plate equation. The measurements are taken on the interface--separating acoustic environment and the elastic wall. Both uniqueness of reconstruction and stability estimates are established. The proofs are based on recently developed Carleman estimates applicable to Neumann unobserved boundaries along with sharp trace regularity results available for wave equations.

Mentor: Irena Lasiecka (University of Virginia)