Inverse force problems for the wave equation
The determinations of an unknown space- or time-dependent force function acting on a vibrating structure from boundary, interior or integral observations are investigated. Sufficient conditions for the uniqueness of solution are provided. These linear inverse force problems are ill-posed since small errors in the input data cause large errors in the output force solution. Consequently, when the input data is contaminated with noise, we use regularization methods, e.g. Tikhonov's regularization, truncated singular value decomposition, or conjugate gradient method, in order to obtain a stable solution. Numerical results will be presented and discussed.