Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article The Problem of Scattering by a Mixture of Cracks and Obstacles | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 524846 19 pages doi 2009 524846 Research Article The Problem of Scattering by a Mixture of Cracks and Obstacles Guozheng Yan Department of Mathematics Central China Normal University Wuhan 430079 China Correspondence should be addressed to Guozheng Yan yamgz@ Received 8 September 2009 Accepted 2 November 2009 Recommended by Salim Messaoudi Consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open crack r and a bounded domain D in R2 as cross section. We assume that the crack r is divided into two parts and one of the two parts is possibly coated on one side by a material with surface impedance X Different boundary conditions are given on r and dD. Applying potential theory the problem can be reformulated as a boundary integral system. We obtain the existence and uniqueness of a solution to the system by using Fredholm theory. Copyright 2009 Guozheng Yan. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Crack detection is a problem in nondestructive testing of materials which has been often addressed in literature and more recently in the context of inverse problems. Early works on the direct and inverse scattering problem for cracks date back to 1995 in 1 by Kress. In that paper Kress considered the direct and inverse scattering problem for a perfectly conducting crack and used Newton s method to reconstruct the shape of the crack from a knowledge of the far-field pattern. In 1997 Monch considered the same scattering problem for sound-hard crack 2 and in the same year Alves and Ha Duong discussed the scattering problem but for flat cracks in 3 . Later in 2000 Kress s work was continued by Kirsch and Ritter in 4 who used the factorization .