The Problem Of Mixed Scattering By An Obstacle And A Crack

In this paper,we focus on the scattering problem of mixed sound waves by con-taining an obstacle and a crack.The domain ? formed by the obstacle is penetrable.The crack r is non-self-intersection.For the sake of achieving numerical implemen-tation,we consider the problem in R².The mixed boundary value problem can be described as:Given _f1 ? H^-1/2??????,f₂? H^-1/2??????,f₃ ?H^1/2???,f₄ ?H^1/2???.Look for functions u ?H_loc¹?R²\??????????and v ? H¹???such that:and the function u satisfy the Sommerfeld radiation condition:uniformly in x = x/|x| with r =|x|.For the above problem,we mainly research the existence and uniqueness.Al-so,we research the inverse problem and reconstruct the obstacle and crack.For the uniqueness of the solution,we can use Rellich lemma to prove it with the help of Green formula.For the existence of the solution,we establish a boundary integral system by using the Green formula and potential theory.Then we can use the Fred-holm theory to prove it.For the reconstruction of the obstacle and crack in inverse scattering problem,we use the Linear sampling method to calculate the far-field in-formation,and then the shape of mixed obstacles are reconstructed with the help of Matlab.