Boundary Value Problems in a Semi-infinite Parallelepiped for an Elliptic Equation with Three Singular Coefficients

Karimov, K. T.

doi:10.1134/s1995080221030124

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Construction Of Particular Solutions Of Equation (1) In the ...1

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2022

2024

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Cited by 4 publications

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“…where ω = √ μ, I l (x) is the Bessel function of an imaginary argument of order l [17]. (15) is a hypergeometric Gaussian equation [18]. Its general solution is defined by the formula [18]…”

Section: Construction Of Particular Solutions Of Equation (1) In the ...mentioning

confidence: 99%

A Problem for a Three-Dimensional Equation of Mixed Type With Singular Coefficient

Karimov,

Shokirov

2024

Int. J. of Appl. Math.

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In this paper, we study the spatial Tricomi problem for a three-dimensional equation of mixed type with a singular coefficient in a domain whose elliptical part is a quarter of a cylinder, and whose hyperbolic part is a triangular right prism. The study of the problem is carried out using the method of separation of variables and spectral analysis. The solution to the considered problem is constructed as a sum of a double series. To justify the uniform convergence of the constructed series, asymptotic estimates of the Bessel and Gauss functions were used. On their basis, estimates were obtained for each member of the series, which made it possible to prove the convergence of the resulting series and its derivatives up to the second order inclusive, as well as the existence theorem in the class of regular solutions.

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Section: Construction Of Particular Solutions Of Equation (1) In the ...mentioning

confidence: 99%

A Problem for a Three-Dimensional Equation of Mixed Type With Singular Coefficient

Karimov,

Shokirov

2024

Int. J. of Appl. Math.

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The Dirichlet Problem for an Elliptic Equation with Three Singular Coefficients and Negative Parameters

Urinov

Karimov

2023

J Math Sci

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The Neumann Problem for a Multidimensional Elliptic Equation with Several Singular Coefficients in an Infinite Domain

Ergashev

Tulakova²

2022

Lobachevskii J Math

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Boundary Value Problems in a Semi-infinite Parallelepiped for an Elliptic Equation with Three Singular Coefficients

Cited by 4 publications

References 13 publications

A Problem for a Three-Dimensional Equation of Mixed Type With Singular Coefficient

A Problem for a Three-Dimensional Equation of Mixed Type With Singular Coefficient

The Dirichlet Problem for an Elliptic Equation with Three Singular Coefficients and Negative Parameters

The Neumann Problem for a Multidimensional Elliptic Equation with Several Singular Coefficients in an Infinite Domain

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