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

Ivan V. Andronov, Boris P. Belinskiy

Результат исследований: Научные публикации в периодических изданияхстатья

Выдержка

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.

Язык оригиналаанглийский
Страницы (с-по)1176-1202
Число страниц27
ЖурналJournal of Mathematical Analysis and Applications
Том456
Номер выпуска2
DOI
СостояниеОпубликовано - 15 дек 2017

Отпечаток

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

Предметные области Scopus

  • Анализ
  • Прикладная математика

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On the parabolic equation method for the problem of diffraction by strongly elongated spheroid. / Andronov, Ivan V.; Belinskiy, Boris P.

В: Journal of Mathematical Analysis and Applications, Том 456, № 2, 15.12.2017, стр. 1176-1202.

Результат исследований: Научные публикации в периодических изданияхстатья

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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

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