On Some Mathematical Aspects of High-frequency Diffraction by Strongly Elongated Spheroids

The high-frequency asymptotic procedure developed for the diffraction by an elongated body is proved to reduce the initial problem to a mathematically correct boundary-value problem for the parabolic equation. The analogue of "time" ri varies on an interval [ 1, 1]. The problem is considered in the class of functions with not too singular behavior near 11 = 1 and the solution is understood in the frame of limiting absorption principle. Uniqueness theorem is proved and the explicit representation for the solution is checked to satisfy the required properties.