Scattering problem for in homogeneous medium

II SCATTERING PROBLEM FOR AN INHOMEGENEOUS MEDIUM (Ph. D. Thesis) Adil MISIR GAZI UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOLOGY September 1996 ABSTRACT In this thesis the scattering and the inverse scattering problems for time- harmonic acoustic waves in an inhomegeneous penetrable medium has been investigated. First the scattering problem has been reduced to an integral equation and then the existence and the uniqueness of it's solution have been showed by using the compactness of the integral operator corresponding to this integral equation. For the inverse scattering problem, the far-field pattern function F(x;k,a) has been obtained. Next the set 3 = { F(x;k,a) : n = 1, 2, 3, } has been considered and then using the projection theorem, it has been shown that L2 (3Q) = span 3 © 31. Finally sufficient conditions have been given for the class of far-field patterns corresponding to the time-harmonic plane waves to be complete in L2 (dQ), and by the aid of this the existence and the uniqueness of the solution of the interior inhomegeneous transmission problem have been showed. Science Code : 403.06.01 Key Words : Scattering problem, acoustic waves, far-field pattern Page Number : 55 Adviser : Prof. Dr. Î. Ethem ANAR