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Open Access Research Article

The Problem of Scattering by a Mixture of Cracks and Obstacles

Guozheng Yan

Author Affiliations

Department of Mathematics, Central China Normal University, Wuhan 430079, China

Boundary Value Problems 2009, 2009:524846  doi:10.1155/2009/524846

Published: 30 November 2009

Abstract

Consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open crack and a bounded domain in as cross section. We assume that the crack is divided into two parts, and one of the two parts is (possibly) coated on one side by a material with surface impedance . Different boundary conditions are given on and . 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.