Uniqueness And Stability Of Exterior Dirichlet Inverse Scattering Problem

In this paper, we discuss the uniqueness and stability of the inverse Helmholtz equation in the two-Dimensional space:where D(?)R~2 is a bounded domain with sufficiently smooth boundaryΓ.k∈C is a wave number.The aim of this paper is to study the uniqueness and stability of the above inverse scattering problem. By employing the known information of scattering field to completely determine the scatterer,then using the solution of the scattering problem and the corresponding perturbed solution to approximately control the boundary to get the stability of the inverse scattering problem.For the uniqueness of the inverse problem,we get the conclusion of some cases.For the proof of the stability, we firstly get the weak solution with variational pattern and the corresponding equation of solution perturbed, then employ the material derivative to prove the boundary can be approximately controlled.