Inverse Obstacle Scattering with Non-Over-Determined Scattering Data

af Alexander G. Ramm

The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering ¿¿¿¿(¿¿¿¿;¿¿¿¿;¿¿¿¿), where ¿¿¿¿(¿¿¿¿;¿¿¿¿;¿¿¿¿) is the scattering amplitude, ¿¿¿¿;¿¿¿¿ ¿¿¿¿ ¿¿¿¿² is the direction of the scattered, incident wave, respectively, ¿¿¿¿² is the unit sphere in the ¿³ and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensional... (Læs mere)