The Properties Of The Far Field Operator For The Transmission Problem

In this paper, We study a special type of transmission problem which model the scattering of incident plane waves by a penetrable obstacle.Inverse acoustic and electromagnetic scattering theroy is a typical inverse problem of mathematics and physicswhich is widely used in areas such as radar ,sonar,geop-hysical exploration. Firstly we prove existence and uniquense of the direct transmission problem by potential theory and Fredholm theo-rem,Moreover we obtain that the far field patterns of transmission problem is dense in L2(Ω).On the base of the analysis of the direct transmission problem we will study the corresponding inverse problem,and the study of the properties of the far field operator for inverse transmission problem are essential for numerical approximation ,i.e.,from the knowledge of the field patterns to model the shape of the scatterer. We get the normality and the condition of injectivity of the far field operator by the boundary integral equation method.