Determination of the shape of a cavity in an orthotropic half-plane given the wave field at the boundary (Q1316739)

The authors consider the inverse scattering problem arising from vibration of an orthotropic half-plane, containing a convex cavity of unknown shape, due to a time-harmonic point source. The problem gives rise to a system of nonlinear operator equations which, upon linearization, gives two boundary integral equations over a known cavity and a linear integral equation with a smooth kernel. These are then solved numerically using the Tikhonov regularization.