A criterion of uniqueness of a solution to the Dirichlet problem with the axial symmetry for the three-dimensional mixed type equation with the Bessel operator

2014 ◽  
Vol 58 (6) ◽  
pp. 69-73 ◽  
Author(s):  
R. M. Safina
Keyword(s):  
Dirichlet Problem ◽  
Axial Symmetry ◽  
Mixed Type ◽  
Three Dimensional ◽  
Type Equation ◽  
Bessel Operator ◽  
Mixed Type Equation ◽  
Criterion Of Uniqueness ◽  
Uniqueness Of A Solution

A nonlocal boundary-value problem for a fourth-order mixed-type equation

2020 ◽  
Vol 17 (1) ◽  
pp. 30-40
Author(s):  
Kudratillo Fayazov ◽  
Ikrombek Khajiev
Keyword(s):  
Fourth Order ◽  
Mixed Type ◽  
Nonlocal Boundary ◽  
Type Equation ◽  
Small Denominators ◽  
Mixed Type Equation ◽  
The Stability ◽  
Criterion Of Uniqueness ◽  
Uniqueness Of A Solution ◽  
Stability Of The Solution

The criterion of uniqueness of a solution of the problem with periodicity and nonlocal and boundary conditions is established by the spectral analysis for a fourth-order mixed-type equation in a rectangular region. When constructing a solution in the form of the sum of a series, we use the completeness in the space L_2, the system of eigenfunctions of the corresponding problem orthogonally conjugate. When proving the convergence of a series, the problem of small denominators arises. Under some conditions imposed on the parameters of the data of the problem and given functions, the stability of the solution is proved.

scholarly journals The Keldysh problem for a mixed-type three-dimensional equation with three singular coefficients

2021 ◽  
pp. 29-46
Author(s):  
К.Т. Каримов
Keyword(s):  
Uniqueness Theorem ◽  
Mixed Type ◽  
Three Dimensional ◽  
Type Equation ◽  
Rectangular Parallelepiped ◽  
Mixed Type Equation ◽  
One Dimensional ◽  
Singular Coefficients ◽  
Dimensional Equation ◽  
Keldysh Problem

В данной статье изучена задача Келдыша для трехмерного уравнения смешанного типа с тремя сингулярными коэффициентами в прямоугольном параллелепипеде. На основании свойства полноты систем собственных функций двух одномерных спектральных задач, доказана теорема единственности. Решение поставленной задачи построено в виде суммы двойного ряда Фурье-Бесселя. In this article, we study the Keldysh problem for a three-dimensional mixed-type equation with three singular coefficients in a rectangular parallelepiped. Based on the completeness property of systems of eigenfunctions of two one-dimensional spectral problems, a uniqueness theorem is proved. The solution to the problem posed is constructed as the sum of a double Fourier-Bessel series.

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