Direct Acoustic Obstacle Scattering

Abstract

This chapter is devoted to the solution of the direct obstacle scattering problem for acoustic waves. As in [41], we choose the method of integral equations for solving the boundary value problems. However, we decided to leave out some of the details in the analysis. In particular, we assume that the reader is familiar with the Riesz-Fredholm theory for operator equations of the second kind in dual systems as described in [41] and [155]. We also do not repeat the technical proofs for the jump relations and regularity properties for single- and double-layer potentials. Leaving aside these two restrictions, however, we will present a rather complete analysis of the forward scattering problem. For the reader interested in a more comprehensive treatment of the direct problem, we suggest consulting our previous book [41] on this subject.