Abstract

Problems of high-frequency diffraction in convex bodies are of great theoretical and practical interest. For approximate calculations of the field in the illuminated region the method of geometric or physical optics is very often used. This is as follows. A system of rays constructed according to the laws of geometric optics is associated with the reflected wave. Then the phase of the reflected wave is taken to be equal to the length of the ray arriving at the given point, and its amplitude determined from the spread of the radial tubes of the given system of rays. The results obtained by this method agree fairly well with experimental data when the incident wave is of sufficiently high frequency. It is therefore usually considered that the approximation of geometric optics gives the first term of the asymptotic expansion of the exact solution in inverse powers of k ( k is the wave number). There have recently been numerous attempts to find a rigorous mathematical proof of this statement. Some results achieved in this direction for stationary diffraction were reported at the Second All-Union Symposium on Wave Diffraction in Gerky in June 1962. No analogous results for the nonstationary diffraction of waves were obtained. In this paper we consider non-stationary high-frequency diffraction on a smooth convex surface going to infinity. We obtain the expansion of the solution in inverse powers of the wave number (or frequency) of the incident wave in the illuminated region and prove a theorem which states that the resulting expansion is the asymptotic expansion of the exact solution.

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