The Study For The Penetrable Scattering Problem With The Robin Core

In this paper,we consider the penetrable scattering problem with the Robin core,The problem can be attributed to the following mixed boundary value problem:with k_i > 0,j = 0,1;μ> 0,λis the complex function,Re(?)≤0,ηis a H(?)lder continuous function,and (?),η(x)≠0, (?).We separate two parts to research the problem:one is the scattering problem ;the other is the inverse scattering problem,given the shape of the scatterers,to determine the impedance functionηfrom a knowledge of the far field pattern for one incident wave,These two aspects of the study are based on the corresponding boundary integral equation.