| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 93 === In problems dealing with the scattering of acoustic waves, we encounter functions known as scattered fields and far fields . In this article, I will derive the scattered field from a given far field pattern where the total field is
governed by the equation Lu+k^2 u=0 outside a domain D. Here, L is an elliptic operator which coincides with the Laplace operator outside a ball of radius R centered at the origin. The derivation of the scattered field is divided into two parts. First, according to known theory in the scattering of acoustic waves, we can derive the scattered field in the region outside of the ball. Then
with the Cauchy data of the scattered field on the boundary of the ball, we will solve the Cauchy problem for the scattered field in the region inside the ball omitting D, and hence we get the complete scattered field.
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