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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2018, Volume 145, Pages 95–109 (Mi into283)  

This article is cited in 1 scientific paper (total in 1 paper)

On a Boundary-Value Problem for a Fourth-Order Partial Integro-Differential Equation with Degenerate Kernel

T. K. Yuldashev

M. F. Reshetnev Siberian State University of Science and Technologies

Abstract: In this paper, the classical solvability of a nonlocal boundary-value problem for a three-dimensional, homogeneous, fourth-order, pseudoelliptic integro-differential equation with degenerate kernel is proved. The spectral Fourier method based on the separation of variables is used and a countable system of algebraic equations is obtained. A solution is constructed explicitly in the form of a Fourier series. The absolute and uniform convergence of the series obtained and the possibility of termwise differentiation of the solution with respect to all variables are justified. A criterion of unique solvability of the problem considered is ascertained.

Keywords: pseudoelliptic equation, degenerate kernel, integral condition, one valued solvability, classical solution

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Bibliographic databases:
UDC: 517.968
MSC: 35A02, 35M10, 35S05

Citation: T. K. Yuldashev, “On a Boundary-Value Problem for a Fourth-Order Partial Integro-Differential Equation with Degenerate Kernel”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 145, VINITI, M., 2018, 95–109

Citation in format AMSBIB
\Bibitem{Yul18}
\by T.~K.~Yuldashev
\paper On a Boundary-Value Problem for a Fourth-Order Partial Integro-Differential Equation with Degenerate Kernel
\inbook Geometry and Mechanics
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 145
\pages 95--109
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into283}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3824392}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. T. K. Yuldashev, “Integro-differentsialnoe uravnenie s dvumernym operatorom Uizema vysokoi stepeni”, Matematicheskii analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 156, VINITI RAN, M., 2018, 117–125  mathnet
  • Itogi Nauki i Tekhniki. Seriya "Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory" Itogi Nauki i Tekhniki. Seriya "Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory"
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