On a Boundary-Value Problem for a Fourth-Order Partial Integro-Differential Equation with Degenerate Kernel

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 sy...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 245; no. 4; pp. 508 - 523
Main Author Yuldashev, T. K.
Format Journal Article
LanguageEnglish
Published New York Springer US 02.03.2020
Springer
Springer Nature B.V
Subjects
Boundary value problems
Differential equations
Fourier series
Kernels
Mathematical analysis
Mathematics
Mathematics and Statistics
integral condition
pseudoelliptic equation
classical solution
35A02
35M10
degenerate kernel
35S05
unique solvability
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Summary: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 the unique solvability of the problem considered is ascertained.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-04707-2