The three dimensional inverse scattering problem for acoustic waves☆

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Abstract

We consider the inverse scattering problem for an acoustically soft obstacle in R3. By assuming a priori that the unknown scattering obstacle is starlike and has its boundary lying in a compact family of Hölder continuously differentiable surfaces, it is shown that an optimal solution can be constructed which depends continuously on the measured far field data. Remarks are made on the numerical approximation of the optimal solution.

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The research of T.S.A. was supported in part by AFOSR Grant 79-0085 and the research of D.C. was supported in part by AFOSR Grant 81-0103.

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This paper was prepared while T.S.A. was on leave and visiting at Lehrstühle für Numerische und Angewandte Mathematik, Universität Göttingen.

Copyright © 1982 Published by Elsevier Inc.