Keldysh problem for mixed type equation with strong characteristic degeneration and singular coefficient

2017 ◽  
Vol 61 (8) ◽  
pp. 46-54 ◽  
Author(s):  
R. M. Safina
Keyword(s):  
Mixed Type ◽  
Type Equation ◽  
Singular Coefficient ◽  
Mixed Type Equation ◽  
Keldysh Problem

scholarly journals Keldysh problem for Pulkin’s equation in a rectangular domain

2017 ◽  
Vol 21 (3) ◽  
pp. 53-63
Author(s):  
R.M. Safina
Keyword(s):  
Uniform Convergence ◽  
Mixed Type ◽  
Type Equation ◽  
Rectangular Domain ◽  
Regular Solutions ◽  
Singular Coefficient ◽  
Small Denominator ◽  
One Dimensional ◽  
Criterion Of Uniqueness ◽  
Keldysh Problem

In this article for the mixed type equation with a singular coefficient Keldysh problem of incomplete boundary conditions is studied. On the basis of property of completeness of the system of own functions of one-dimensional spectral prob- lem the criterion of uniqueness is established. The solution is constructed as the summary of Fourier-Bessel row. At the foundation of the uniform convergence of a row there is a problem of small denominators.Under some restrictions on these tasks evaluation of separation from zero of a small denominator with the corresponding asymptotics was found, which helped to prove the uniform con- vergence and its derivatives up to the second order inclusive, and the existence theorem in the class of regular solutions.

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.

scholarly journals A boundary value problem for mixed type equation with singular coefficient

2021 ◽  
pp. 27-39
Author(s):  
М.Х. Рузиев ◽  
Ф.С. Актамов
Keyword(s):  
Boundary Value Problem ◽  
Integral Equations ◽  
Unique Solvability ◽  
Mixed Type ◽  
Boundary Value ◽  
Type Equation ◽  
Singular Coefficient ◽  
Mixed Type Equation ◽  
Method Of Integral Equations ◽  
Principle Of Extremum

В работе изучается краевая задача для уравнения смешанного типа с сингулярным коэффициентом в области, эллиптической частью которой является первая четверть плоскости, а гиперболической частью — характеристический треугольник. Методами интегральных уравнений и принципа экстремума доказывается однозначная разрешимость рассматриваемой задачи. In this paper we study a boundary value problem for a mixed type equation in a domain whose elliptic part is the first quadrant of the plane and the hyperbolic part is the characteristic triangle. With the help of the method of integral equations and the principle of extremum we prove the unique solvability of the considered problem

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