General form of the Euler-Poisson-Darboux equation and application of the transmutation method

In this article, we find solution representations in the compact integral form to the Cauchy problem for a general form of the Euler-Poisson-Darboux equation with Bessel operators via generalized translation and spherical mean operators for all values of the parameter k, including also not studying before exceptional odd negative values. We use a Hankel transform method to prove results in a unified way. Under additional conditions we prove that a distributional solution is a classical one too. A transmutation property for connected generalized spherical mean is proved and importance of applying transmutation methods for differential equations with Bessel operators is emphasized. The paper also contains a short historical introduction on differential equations with Bessel operators and a rather detailed reference list of monographs and papers on mathematical theory and applications of this class of differential equations. © 2017 Texas State University.

Авторы
Shishkina E.L.1 , Sitnik S.M. 2, 3
Редакторы
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Издательство
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Номер выпуска
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Язык
Английский
Страницы
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Статус
Опубликовано
Подразделение
-
DOI
-
Номер
177
Том
2017
Год
2017
Организации
  • 1 Voronezh State University, Faculty of Applied Mathematics, Informatics and Mechanics, Universitetskaya square, 1, Voronezh, 394006, Russian Federation
  • 2 Institute of Engineering Technology and Natural Science, Belgorod State National Research University, Pobedy str., 85, Belgorod, 308015, Russian Federation
  • 3 RUDN University, 6 Miklukho-Maklaya st, Moscow, Russian Federation
Ключевые слова
Bessel operator; Euler-Poisson-Darboux equation; Hankel transform; Transmutation operators
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5419/