Inverse problem for structural acoustic interaction

✍ Scribed by Shitao Liu

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 383 KB
• Volume: 74
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2010.12.020

✦ Synopsis

We consider an inverse problem of determining a source term for a structural acoustic partial differential equation (PDE) model that is comprised of a two-or a three-dimensional interior acoustic wave equation coupled to an elastic plate equation. The coupling takes place across a boundary interface. For this PDE system, we obtain uniqueness and stability estimates for the source term from a single measurement of boundary values of the ''structure'' (acceleration of the elastic plate). The proof of uniqueness is based on a Carleman estimate (first version) of the wave problem within the chamber. The proof of stability relies on three main points: (i) a more refined Carleman estimate (second version) and its resulting implication, a continuous observability-type estimate; (ii) a compactness/uniqueness argument; (iii) an operator theoretic approach for obtaining the needed regularity in terms of the initial conditions.