The Scattering Problem Of Mixed Obstacles With Cracks

In this paper, we mainly study the scattering problem of electromagnetic waves having a obstacle with a crack. The horizontal cross section is composed by a smooth bounded boundary D and an arc Γ. In the end, the scattering problem can be formulated as a mixed boundary value by Helmholtz equation in R2:Given f∈H-1/2((?)D), h ∈ H-1/2(Γ), find a function u ∈ Hloc1R2\(D∪Γ)) such that and the scattered field u is required to satisfy the well-known Sommerfeld Radiation condition uniformly inFor the above problem, we mainly research the existence and uniqueness of the solution to the problem. The uniqueness of the solution to the problem can be directly obtained by Rellich lemma. We obtain the existence of the solution to the problem by boundary integral system method. That is, we establish a boundary integral system by using the Green’s representation formula and potential theory. Then by the Fredholm theory, we obtain the the existence and uniqueness of the solution to the boundary integral system, and then the existence of the solution to the original direct scattering problem are obtained.In the last section of this article, having introduced the steps of linear sampling method for solving the inverse scattering problem simply.