Geodesic
On a Boundary-Value Problem for a Fourth-Order Partial Integro-Differential Equation with Degenerate Kernel
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 145 (2018), pp. 95-109

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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 unique solvability of the problem considered is ascertained.
Mots-clés : pseudoelliptic equation
Keywords: degenerate kernel, integral condition, one valued solvability, classical solution. 
@article{INTO_2018_145_a2,
     author = {T. K. Yuldashev},
     title = {On a {Boundary-Value} {Problem} for a {Fourth-Order}  {Partial} {Integro-Differential} {Equation} with {Degenerate} {Kernel}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {95--109},
     publisher = {mathdoc},
     volume = {145},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_145_a2/}
}
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T. K. Yuldashev. On a Boundary-Value Problem for a Fourth-Order  Partial Integro-Differential Equation with Degenerate Kernel. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 145 (2018), pp. 95-109. http://geodesic.mathdoc.fr/item/INTO_2018_145_a2/