Behaviour of (−Δ−k2−i0+)−1 outside fading obstacles,independant scattering hypothesis and applications

This paper deals with the behaviour of k‐outgoing solutions of ?Δu?k²u=f outside a fading soft obstacle. We extend an approach using the so‐called Lax–Phillips construction and the well‐known properties of the capacity of smooth obstacles. So, classical results are recovered in a straightforward manner. The previous approach enables us to consider the case of obstacles composed of many tiny spheres. Roughly speaking, we prove that the scattering amplitude is approximately the sum of the scattering amplitudes scattered by each isolated sphere, which is an alternative form of the first Born approximation. As a consequence, two inverse problems are solved. Copyright © 2003 John Wiley & Sons, Ltd.