The Scattering Problem For Mixed Partially Coated Obstacles

This thesis has mainly studied the mixed acoustic scattering problems with a pen-etrable obstacle and a partially coated impenetrable obstacle.Suppose D is bounded and penetrable,its boundary is smooth,D1 is bounded and impenetrable,its bound-ary is partially coated,the boundary of D1 is divided into ?1 and E2.We only study the problem in the area R2,in which the mixed boundary value problem is described as following:We should seek u? Hloc1(R2\D U D1)and v ? H1(D)satisfy the following problem:Among this question,u = ui + us,us satisfies lim(?)((?)us/(?)?-ik0us)= 0,r =|x|,this convergence of x =x/|x|,is consistent.Next,we study the above problem from two perspectives.One is the direct scattering problem,which is the existence and uniqueness to the above mixed bound-ary value problem.The uniqueness of solution to the above question can be proved by the Green formula and the Rellich s lemma.The existence of solutions to this problem can be addressed by the boundary integral equation method.The original problem can be transformed into its boundary integral equations by potential theory.The existence and uniqueness of solution to the boundary integral equations can be resolved by the Fredholm alternative theorem,therefore the solution of the original problem is existed.The other is the inverse scattering problem.Firstly,we should establish the far-field data.Then the shape.s of D and D1 can be reconstructed by the far-field data.We can solve this proble.m by the linear sampling method.