The Problem Of Scattering By Two Cracks And An Obstacle

In this paper,we focuses on the scattering problem of mixed sound waves by containing two cracks and an obstacle.The domain ?0 formed by the obstacle is penetrable.The two cracks ?1??2 are non-self-intersection and disjoint.For the sake of achieving numerical implementation,we consider the problem only in R2.The direct problem can be described as:We suppose h0?H-1/2(?)?0),h1?(?1),h?1/2(?2)),h3? H-1/2(?2),my work is to find a function u ? H1(?0)?Hloc1(R2\?0??1??2)meeting those con ditions:where r = |x|,and the convergence holds uniformly in x = x/|x|.The main contents of this paper contains:we can use the Rellich's lemma to prove the uniqueness of the direct problem;we can use the boundary integral equation method to prove the existence of the direct problem;we can use the Linear sampling method to solve the inverse problem and reconstruct the obstacle and cracks.