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

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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 the unique solvability of the problem considered is ascertained.

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Authors and Affiliations

  1. M. F. Reshetnev Siberian State University of Science and Technologies, Krasnoyarsk, Russia

    T. K. Yuldashev

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  1. T. K. Yuldashev
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Correspondence to T. K. Yuldashev.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 145, Geometry and Mechanics, 2018.

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Yuldashev, T.K. On a Boundary-Value Problem for a Fourth-Order Partial Integro-Differential Equation with Degenerate Kernel. J Math Sci 245, 508–523 (2020). https://doi.org/10.1007/s10958-020-04707-2

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  • DOI: https://doi.org/10.1007/s10958-020-04707-2

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