Positive Scattering Problem Of Penetrable Scatterers With Mixed Transmission Conditions

Acoustic scattering widely exists in geological exploration,medical imaging,non-destructive testing and other application fields.This paper mainly studies two types of positive acoustic scattering problems,one type is a scatterer that can penetrate an obstacle with an extremely thin body in an ideal state at the boundary,and the other is a scatterer that has mixed transmission conditionsand.We use the method of boundary integral equation to explore the existence,uniqueness and continuous dependence of the solutions of these two different kinds of scatterers.Although the methods used are the same,there are still differences in details.In general,this article first uses the Green's formula and Rellich's lemma to find the uniqueness of the solution to the positive scattering problem.Based on the potential theory,the two types of scatterers are introduced into the form of boundary integral equations,and then use Fredholm's theorem to prove its existence and uniqueness,This indirectly proves the well-posedness of the original positive scattering problem.