Geodesic
On features of the solution of a boundary-value problem for the multidimensional integro-differential Benney--Luke equation with spectral parameters
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 174 (2020), pp. 109-129

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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
Mots-clés : construction of solutions. 
@article{INTO_2020_174_a8,
     author = {T. K. Yuldashev},
     title = {On features of the solution of a boundary-value problem for the multidimensional integro-differential {Benney--Luke} equation with spectral parameters},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {109--129},
     publisher = {mathdoc},
     volume = {174},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_174_a8/}
}
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T. K. Yuldashev. On features of the solution of a boundary-value problem for the multidimensional integro-differential Benney--Luke equation with spectral parameters. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 174 (2020), pp. 109-129. http://geodesic.mathdoc.fr/item/INTO_2020_174_a8/