The Mixed Scattering Problem For A Class Of Layered Media And An Impenetrable Obstacle

In this paper,We focus on the mixed scattering of a kind of layered medium and an impenetrable obstacle.The layered medium ?2 is disjoint with the impenetrable obstacle ?3.And there will be an impenetrable obstacle ?1 in the layered media ?2.The paper will study this problem in R2,then:Given h1?H1/2((?)?2),h2 ? H-1/2((?)?2),h3?H1/2((?)?3),Look for function u?Hloc1(R2\(?)2?(?)3)),v?H1(?2\(?)1)satisfy:and the scattered field u satisfies the Sommerfeld Radiation condition:where r?|x|,and the convergence holds uniformly in (?)=x/|x|.For this problem,this paper mainly studies the existence and uniqueness of the solution of the positive scattering problem and the corresponding inverse scattering problem that is the shapes of the obstacle reconstructed by the far-field information.The uniqueness of the solution of the positive problem is obtained by using Green's formula and Rellich lemma,and the existence of the solution is obtained by using Green theorem and potential theory,The appropriate variables are set,and the ap-propriate boundary integral equations are obtained by using boundary conditions,Then,it is proved that the equations have solution,and then the original problem has solution.The obstacles reconstruction in the inverse scattering problem adopt the linear sampling method,Finally,a numerical simulation example is given and the shape of the mixed obstacles are reconstructed by Matlab.