On fundamental solutions for 3D singular elliptic equations with a parameter

Urinov, A. K.; Karimov, Erkinjon

doi:10.1016/j.aml.2010.10.013

Cited by 11 publications

(7 citation statements)

References 8 publications

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“…Recently, I.T.Nazipov published a paper devoted to the investigation of the Tricomi problem in a mixed domain consisting of hemisphere and cone [16]. We also note works [17][18][19], where fundamental solutions and boundary problems for elliptic equations with three singular coefficient were subject of investigation. By J.J.Nieto and E.T.Karimov [20] the Dirichlet problem for an equation…”

Section: Introductionmentioning

confidence: 95%

Spatial boundary problem with the Dirichlet–Neumann condition for a singular elliptic equation

Салахитдинов

Karimov

2012

Applied Mathematics and Computation

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The present work devoted to the finding explicit solution of a boundary problem with the Dirichlet-Neumann condition for elliptic equation with singular coefficients in a quarter of ball. For this aim the method of Green's function have been used. Since, found Green's function contains a hypergeometric function of Appell, we had to deal with decomposition formulas, formulas of differentiation and some adjacent relations for this hypergeometric function in order to get explicit solution of the formulated problem.

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Section: Introductionmentioning

confidence: 95%

Spatial boundary problem with the Dirichlet–Neumann condition for a singular elliptic equation

Салахитдинов

Karimov

2012

Applied Mathematics and Computation

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“…Various modifications of the equation (1) in the two-and three-dimensional cases were considered in many papers [4,[18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Fundamental Solutions for a Class of Multidimensional Elliptic Equations with Several Singular Coefficients

Ergashev

Эргашев²

2020

Journal of Siberian Federal University. Mathematics &Amp; Physics

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The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients. These fundamental solutions are directly connected with multiple hypergeometric functions and the decomposition formula is required for their investigation which would express the multivariable hypergeometric function in terms of products of several simpler hypergeometric functions involving fewer variables. In this paper, such a formula is proved instead of a previously existing recurrence formula.The order of singularity and other properties of the fundamental solutions that are necessary for solving boundary value problems for degenerate second-order elliptic equations are determined

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“…Various modifications of equation (1.1) in the two-and three-dimensional cases were considered in many papers [6,7,8,5]. However, relatively few papers have been devoted to finding the fundamental solutions when the dimension of equation exceeds three, we only note the works [5,9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variables

Ergashev¹

2019

Preprint

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In this paper, we introduce a new class of confluent hypergeometric functions of many variables, study their properties, and determine a system of partial differential equations that this function satisfies. It turns out that all the fundamental solutions of the generalized Helmholtz equation with several singular coefficients are written out through the newly introduced confluent hypergeometric function. Using the expansion formula established here for the confluent function, the order of the singularity of the fundamental solutions of the elliptic equation under this consideration is determined.

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On fundamental solutions for 3D singular elliptic equations with a parameter

Cited by 11 publications

References 8 publications

Spatial boundary problem with the Dirichlet–Neumann condition for a singular elliptic equation

Spatial boundary problem with the Dirichlet–Neumann condition for a singular elliptic equation

Fundamental Solutions for a Class of Multidimensional Elliptic Equations with Several Singular Coefficients

Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variables

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