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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2022, Volume 26, Number 2, Pages 273–292
DOI: https://doi.org/10.14498/vsgtu1893
(Mi vsgtu1893)
 

This article is cited in 3 scientific papers (total in 3 papers)

Differential Equations and Mathematical Physics

An initial boundary value problem for a partial differential equation of higher even order with a Bessel operator

A. K. Urinovab, M. S. Azizova

a Fergana State University, Fergana, 150100, Uzbekistan
b Institute of Mathematics named after V. I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan, Tashkent, 100174, Uzbekistan (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: In present paper, an initial-boundary value problem is formulated in a rectangle for a higher even order partial differential equation with the Bessel operator. Applying the method of separation of variables to the considered problem a spectral problem is obtained for an ordinary differential equation of higher even order. The self-adjointness of the last problem is proved, which implies the existence of the system of its eigenfunctions, as well as the orthonormality and completeness of this system. The uniform convergence of some bilinear series and the order of the Fourier coefficients, depending on the found eigenfunctions, is investigated. The solution of the considered problem is found as the sum of the Fourier series with respect to the system of eigenfunctions of the spectral problem. The absolute and uniform convergence of this series, as well as the series obtained by its differentiating, have been proved. The uniqueness of the solution of the problem is proved by the method of spectral analysis. An estimate is obtained for the solution of the problem which implies the continuous dependence of the solution on the given functions.
Keywords: even order partial differential equation, Bessel operator, initial-boundary value problem, spectral method, Green's function, integral equation, existence, uniqueness and stability of the solution.
Received: October 29, 2021
Revised: March 9, 2022
Accepted: March 12, 2022
First online: May 23, 2022
Bibliographic databases:
Document Type: Article
UDC: 517.956
MSC: 35G15
Language: Russian
Citation: A. K. Urinov, M. S. Azizov, “An initial boundary value problem for a partial differential equation of higher even order with a Bessel operator”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 26:2 (2022), 273–292
Citation in format AMSBIB
\Bibitem{UriAzi22}
\by A.~K.~Urinov, M.~S.~Azizov
\paper An initial boundary value problem for a partial differential equation of higher even order with a Bessel operator
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2022
\vol 26
\issue 2
\pages 273--292
\mathnet{http://mi.mathnet.ru/vsgtu1893}
\crossref{https://doi.org/10.14498/vsgtu1893}
\edn{https://elibrary.ru/LKMGUE}
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  • https://www.mathnet.ru/eng/vsgtu/v226/i2/p273
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
     
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