An inverse source problem for the wave equation Original Research Article

The Cauchy problem for the wave equation, with an unknown source of the form q(t)δ(∂G), is studied. Using control techniques, the generalized Clarke gradients, feedback laws are established, yielding q and the surface ∂G with given observed values of the solution on a portion of a fixed closed surface. The intensity of the source, the shape of the surface are considered as two interacting controls. The problem of the identification of an obstacle from reflected waves have important practical applications in many fields.