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

Ivan V. Andronov, Boris P. Belinskiy

Research output

Abstract

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.

Original languageEnglish
Pages (from-to)1176-1202
Number of pages27
JournalJournal of Mathematical Analysis and Applications
Volume456
Issue number2
DOIs
Publication statusPublished - 15 Dec 2017

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Parabolic Equation
Diffraction
Location of Zeros
Whittaker Function
Formal Solutions
Acoustics
Classical Solution
Justify
Asymptotic Properties
Continuation
Uniqueness

Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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AB - 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.

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KW - Fourier series

KW - Parabolic equation method

KW - Whittaker functions

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