An approximation problem in inverse scattering theory |
| |
Authors: | David Colton Andreas Kirsch |
| |
Affiliation: | 1. Department of Mathematical Sciences , University of Delaware , Newark, Delaware, 19716, USA;2. Institut fur Angewandte Mathematik , Universitaüt Erlangen , Erlangen, D-8520, West Germany |
| |
Abstract: | In [3] a new method was introduced for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium. This method is based on the solution of a new class of boundary value problems for the reduced wave equation called interior transmission problems. In this paper it is shown that if there is absorption there exists at most one solution to the interior transmission problem and an approximate solution can be found such that the metaharmonic part is a Herglotz wave function. These results provide the necessary theoretical basis for the inverse scattering method introduced in [3] |
| |
Keywords: | 35P25 35R30 |
|
|