Geodesic
Boussinesq integro-differential equation with integral conditions and a small coefficient of mixed derivatives
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 211 (2022), pp. 114-130

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In this paper, we prove the unique solvability of a nonlocal boundary-value problem for a high-order, three-dimensional, linear Boussinesq integro-differential equation with a degenerate kernel and general integral conditions and construct a solution in the form of a Fourier series. The absolute and uniform convergence of the resulting series and the possibility of term-by-term differentiation of the solution with respect to all variables are established. A criterion for the unique solvability of the boundary-value problem in the case of regular values of the parameter is obtained. For irregular values of the parameter, an infinite set of solutions is constructed in the form of a Fourier series.
Keywords: integro-differential equation, mixed derivative, unique solvability, integral condition, degenerate kernel.
Mots-clés : Boussinesq equation 
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     title = {Boussinesq integro-differential equation with integral conditions and a small coefficient of mixed derivatives},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
     volume = {211},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_211_a7/}
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T. K. Yuldashev; F. D. Rakhmonov; A. S. Ismoilov. Boussinesq integro-differential equation with integral conditions and a small coefficient of mixed derivatives. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 211 (2022), pp. 114-130. http://geodesic.mathdoc.fr/item/INTO_2022_211_a7/