Parabolic Equation Method for High-frequency Diffraction by an Elongated Body

The high-frequency asymptotic procedure developed for the diffraction by an elongated body is reduced to a mathematically correct boundary-value problem for a parabolic equation. The analogue of "time" eta varies on an interval [-1, 1]. The problem is considered in the class of functions with not too singular behavior near eta = +/- 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.