### 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 language | English |
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Pages (from-to) | 1176-1202 |

Number of pages | 27 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 456 |

Issue number | 2 |

DOIs | |

Publication status | Published - 15 Dec 2017 |

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### Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*456*(2), 1176-1202. https://doi.org/10.1016/j.jmaa.2017.07.029

}

*Journal of Mathematical Analysis and Applications*, vol. 456, no. 2, pp. 1176-1202. https://doi.org/10.1016/j.jmaa.2017.07.029

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

Research output

TY - JOUR

T1 - On the parabolic equation method for the problem of diffraction by strongly elongated spheroid

AU - Andronov, Ivan V.

AU - Belinskiy, Boris P.

PY - 2017/12/15

Y1 - 2017/12/15

N2 - 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.

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.

KW - Diffraction

KW - Fourier series

KW - Parabolic equation method

KW - Whittaker functions

UR - http://www.scopus.com/inward/record.url?scp=85026379240&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2017.07.029

DO - 10.1016/j.jmaa.2017.07.029

M3 - Article

AN - SCOPUS:85026379240

VL - 456

SP - 1176

EP - 1202

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -