传输问题远场算子的性质

对声波与电磁波的逆散射问题（反问题），相应远场算子性质的研究是很重要的，因为它直接关系到未知散射体形状的重构．本文主要讨论一类声波的传输问题，重点研究了其相应远场算子的正则性和单射性条件．当然，反问题与相应的正问题有紧密联系．利用位势理论和Fredholm定理，也证明了相应的正传输问题解的存在和唯一性．

The properties of the far field operator for the transmission problem

To the inverse acoustic and electromagnetic scattering theroy, the study of the properties of the corresponding far field operator for inverse transmission problem are essential for numerical approximation, i. e., from the knowledge of the field patterns to the shape of the scattering. This paper studies a special type of transmission problem which model the scattering of incident plane waves by a penetrable obstacle. It gets the normality and the condition of infectivity of the far field operator by the boundary integral equation method. Studying an inverse problem always requires a solid knowledge of the theory for the corresponding direct problem. It proves the existence and uniqueness of the direct transmission problem by potential theory and Fredholm theorem.