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 Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2020, Volume 174, Pages 109–129 (Mi into571)

On features of the solution of a boundary-value problem for the multidimensional integro-differential Benney–Luke equation with spectral parameters

T. K. Yuldashev

Irkutsk State University

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.

Keywords: boundary-value problem, Fourier series, integral condition, spectral parameter, solvability, construction of solutions

DOI: https://doi.org/10.36535/0233-6723-2020-174-109-129

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UDC: 517.956
MSC: 35A02, 35M10, 35S05

Citation: T. K. Yuldashev, “On features of the solution of a boundary-value problem for the multidimensional integro-differential Benney–Luke equation with spectral parameters”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 174, VINITI, Moscow, 2020, 109–129

Citation in format AMSBIB
\Bibitem{Yul20} \by T.~K.~Yuldashev \paper On features of the solution of a boundary-value problem for the multidimensional integro-differential Benney--Luke equation with spectral parameters \inbook Geometry and Mechanics \serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. \yr 2020 \vol 174 \pages 109--129 \publ VINITI \publaddr Moscow \mathnet{http://mi.mathnet.ru/into571} \crossref{https://doi.org/10.36535/0233-6723-2020-174-109-129} 

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