2010/10/13 by Shitao Liu, Liu, Shitao
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.1010.2695
arxiv created 2010/10/13 · arxiv updated 2010/10/14
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.