Solution of the spatial Tricomi problem for a singular mixed-type equation by the method of integral equations

Nazipov, I. T.

doi:10.3103/s1066369x1103008x

Cited by 10 publications

(8 citation statements)

References 3 publications

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“…The Tricomi problem for a mixed elliptic-hyperbolic equation in threedimensional space using the method of integral Fourier transform was first studied in [3]. After this work, a number of works appeared in which boundary value problems for various elliptic-huperbolic equations in three-dimensional domains were considered (see, for example, [4], [5], [6], [7], [8], [9], [10], [11], [12]).…”

Section: Introduction Problem Statementmentioning

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: Introduction Problem Statementmentioning

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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“…Dirichlet and Dirichlet-Neumann problems for elliptic equation with one singular coefficient in some part of ball were investigated by Agostinelli [1] and Olevskii [26]. Recently, Nazipov published a paper devoted to the investigation of the Tricomi problem in a mixed domain consisting of hemisphere and cone [23]. Fundamental solutions for the following three-dimensional elliptic equations with two and three singular coefficients…”

Section: Introductionmentioning

confidence: 99%

The Dirichlet problem for elliptic equation with several singular coefficients

Ergashev¹

2019

Preprint

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Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the Dirichlet problem for an elliptic equation with several singular coefficients in explicit form. When finding a solution, we use decomposition formulas and some adjacent relations for the Lauricella hypergeometric function in many variables, as well as the values of some multidimensional improper integrals.

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“…Dirichlet and Dirichlet-Neumann problems for elliptic equation with one singular coefficient in some part of ball were investigated by Agostinelli [1] and Olevskii [27]. Recently, Nazipov published a paper devoted to the investigation of the Tricomi problem in a mixed domain consisting of hemisphere and cone [25]. Fundamental solutions for the following three-dimensional elliptic equations with two and three singular coefficients…”

Section: Introductionmentioning

confidence: 99%

“…= 0.If we consider an integralCρ x (2α) G (x; ξ)∂u (x) ∂n dC ρ , using above given algorithm for evaluations (in this case calculations will be more simple), we can prove that lim ρ→0 Cρx (2α) G (x; ξ) ∂u (x) ∂n dC ρ = 0. 96 T. G. ErgashevNow from(25) we can write the solution of the Dirichlet problem as follows: · · · , x k−1 , 0, x k+1 , · · · , x m ; ξ) τ k (x k ) dS k + S x (2α) ∂G (x; ξ) ∂n ϕ (x) dS.…”

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confidence: 99%