An inverse acoustic scattering problem for an obstacle with an impedance boundary condition
This interesting paper is concerned with the two-dimensional inverse problem of plane, time-harmonic wave diffraction by a bounded obstacle on the surface of which an impedance condition is imposed. The aim of the paper is to find a method for determining (approximately) both the shape of the obstacle and the surface impedance from the scattered far field data. Given the low-frequency patterns of the scattered fields resulting from diffraction of three plane waves on the obstacle, the author shows that the problems of determining the scatterer shape and the surface impedance can be isolated and solved successively. In his analysis he uses integral equation methods to represent the scattered field and conformal mapping approach to describe the scatterer shape. He shows the way in which this shape can be determined from the knowledge of the Fourier series expansion of the low-frequency, scattered far field patterns. For the surface impedance the author obtains a Fredholm equation of the first kind. He pays special attention that the problem of finding the impedance be well-posed.
scientific article; zbMATH DE number 3910954
scientific article