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On Features of the Solution of a Boundary-Value Problem for the Multidimensional Integro-Differential Benney–Luke Equation with Spectral Parameters

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Abstract

In this paper, we consider the problems on the solvability and constructing solutions of one nonlocal boundary-value problem for the multidimensional, fourth-order, integro-differential Benney–Luke equation with degenerate kernel and spectral parameters. For various values of spectral parameters, necessary and sufficient conditions of the existence of a solution are obtained. The Fourier series for solutions of the problem corresponding to various sets of spectral parameters are obtained. For regular values of spectral parameters, the absolute and uniform convergence of the series and the possibility of their termwise differentiation with respect to all variables are proved. The problem is also examined studied for cases of irregular values of spectral parameters.

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  1. Irkutsk State University, Irkutsk, 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. 174, Geometry and Mechanics, 2020.

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Yuldashev, T.K. On Features of the Solution of a Boundary-Value Problem for the Multidimensional Integro-Differential Benney–Luke Equation with Spectral Parameters. J Math Sci 272, 729–750 (2023). https://doi.org/10.1007/s10958-023-06467-1

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