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Inverse Problem for a Structural Acoustic Interaction

In this work, we consider an inverse problem of determining a source term for a structural acoustic partial differentia equation (PDE) model, comprised of a two or three-dimensional interior acoustic wave equation coupled to a Kirchoff plate equation, with the coupling being accomplished across a boundary interface. For this PDE system, we obtain the uniqueness and stability estimate for the source term from a single measurement of boundary values of the "structure". The proof of uniqueness is based on Carleman estimate. Then, by means of an observability inequality and a compactness/uniqueness argument, we can get the stability result. Finally, an operator theoretic approach gives us the regularity needed for the initial conditions in order to get the desired stability estimate.