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.
Highlights
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
In 2003, Cakoni and Colton in 5 considered the direct and inverse scattering problem for cracks which possibly coated on one side by a material with surface impedance λ
In the following we just consider the direct scattering problem for a mixture of a crack Γ and a bounded domain D, and the corresponding inverse scattering problem can be considered by similar methods in [1, 2, 4,5,6,7,8,9,10,11,12] and the reference therein
Summary
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. 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 the following we just consider the direct scattering problem for a mixture of a crack Γ and a bounded domain D, and the corresponding inverse scattering problem can be considered by similar methods in [1, 2, 4,5,6,7,8,9,10,11,12] and the reference therein. We will use the method of boundary integral equations and Fredholm theory to obtain the existence and uniqueness of a solution. The potential theory and Fredholm theory will be used to prove our main results
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