Universal Journal of Mathematics and Mathematical Sciences
Volume 4, [Proceedings of International Conference: Mathematical Science and Applications, December 26-30, 2012, Abu Dhabi, UAE] Issue 1, Pages 35 - 49
(July 2013)
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DIRECT AND INVERSE SCATTERING PROBLEM IN PERTURBED HALF-PLANE
B. Berhail and L. Chorfi
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Abstract: We consider in this work a direct and inverse problem in scattering theory. We construct an arc g of the boundary from the far field pattern of the scattered wave at fixed energy. This leads to the direct scattering problem for the Helmholtz equation in a perturbed half-plane with Dirichlet condition on the boundary. Using the integral method, we show that the direct problem is well posed. For the identification of the arc, we prove a uniqueness theorem by using the point source method and a reciprocity relation. |
Keywords and phrases: scattering theory, far field, inverse problem, integral equation method. |
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