On the parabolic equation method for the problem of diffraction by strongly elongated spheroid

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:456

Article

Andronov, Ivan V.¹  Belinskiy, Boris P.² 

[1] St Petersburg State Univ, 1-1 Ulianovskaya Str, Petrodvorets 198504, Russia

[2] Univ Tennessee, Dept Math, Dept 6956,615 McCallie Ave, Chattanooga, TN 37403 USA

关键词: Parabolic equation method;    Diffraction;    Fourier series;    Whittaker functions;   

DOI  :  10.1016/j.jmaa.2017.07.029

来源: Elsevier

【 摘 要 】

Previously, the parabolic equation method was used to study the high-frequency acoustic diffraction by a strongly elongated spheroid. This paper represents a continuation of that study. We justify some formal steps of the parabolic equation method at the level typical for the general PDE theory. In particular, we prove that a formal solution of the parabolic equation is actually the classical solution. We prove its uniqueness. We use various asymptotic properties of the higher functions. Some of these properties are new. We study location of zeros of the Whittaker functions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free