Mixed Scattering Problems With Impenetrable Obstacle Cores In Penetrable Obstacles

The thesis studies a mixed scattering problem that contains impenetrable ob-stacle cores in penetrable obstacles.Assume that D0 is a penetrable obstacle and the boundary αD0 is smooth,which contains an impenetrable obstacle D1 inside,and the boundary αD1 is also smooth.There is an impenetrable obstacle D2 with a partial coating on the outside of D0.The boundary of D2 is composed of two parts τ1 and τ2,each with different boundary conditions.To facilitate the numerical simulation of inverse scattering problem,We only study this problem in the area R2,the description of the positive problem is as follows:We should seek u ∈ Hloc1(R2\D0∪D2)and v E H1(D0∪D1)satisfy the following problem:Among this question,u=ui+us,ui=eik1x·d is the plane wave incident field,which d is the direction of incidence,|d|=1,and the scattering field us satisfies thesommerfeld attenuation condition.us satisfies(?),r=|x|,thisconvergence of x=x|x| is consistent.For the problem,we discuss it in two parts.The first part is to study the well-posedness of the solution of the forward scattering problem.By Rellich lemma prove the uniqueness of the solution;then using Green’s representation theorem construct the general form of the solution.Equivalent boundary integral equations are deduced by potential theory to prove the existence of solutions.The second part is the inverse scattering problem,using the linear Sampling Method obtain Far-field information reconstruction obstacles.