scholarly journals On a semi-nonlocal boundary value problem for the three-dimensional Tricomi equation of an unbounded prismatic domain

2021 ◽  
pp. 8-16
Author(s):  
С.З. Джамалов ◽  
Р.Р. Ашуров ◽  
Х.Ш. Туракулов
Keyword(s):  
Boundary Value Problem ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Three Dimensional ◽  
Generalized Solution ◽  
Nonlocal Boundary Value Problem ◽  
Tricomi Equation ◽  
The Fourier Transform

В данной статье изучаются методами «ε-регуляризации» и априорных оценок с применением преобразования Фурье однозначная разрешимость и гладкость обобщенного решения одной полунелокальной краевой задачи для трехмерного уравнения Трикоми в неограниченной призматической области. In this article, the methods of «ε-regularization» and a priori estimates using the Fourier transform are studied the unique solvability and smoothness of the generalized solution of one semi-nonlocal boundary value problem for the three-dimensional Tricomi equation in an unbounded prismatic domain.

A priori estimate for the solution of a nonlocal boundary value problem for the McKendrick - von Foerster equation of fractional order

2020 ◽  
Vol 20 (1) ◽  
pp. 9-14
Author(s):  
R.Z. Berezgova ◽  
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
A Priori Estimate ◽  
Time Variable ◽  
Nonlocal Boundary Value Problem ◽  
Priori Estimate

In this paper, by the method of energy inequalities, an a priori estimate for the solution of the nonlocal boundary value problem is obtained for the generalized Mackendrick - von Foerster equation with the Caputo operator with respect to the time variable.

scholarly journals A PRIORI ESTIMATION OF A GENERALIZED NONLOCAL BOUNDARY VALUE PROBLEM FOR A THRID ORDER EQUATION WITH A FRACTIONAL TIME CAPUTO DERIVATIVE

2019 ◽  
pp. 35-40
Author(s):  
А.М. Шхагапсоев
Keyword(s):  
Boundary Value Problem ◽  
Caputo Derivative ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Fractional Caputo Derivative ◽  
Multiple Characteristics ◽  
A Priori Estimation

Рассматривается краевая задача для уравнения третьего порядка параболического типа с дробной производной Капуто. Методом энергетических неравенств получена априорная оценка решения обобщенной нелокальной краевой задачи для уравнения с кратными характеристиками с дробной производной Капуто по времени. A boundary value problem for a third-order parabolic equation with a fractional Caputo derivative is considered. A priori estimation of the solution of a generalized nonlocal boundary value problem for an equation with multiple characteristics with a fractional Caputo derivative in time is obtained by the method of energy inequalities.

scholarly journals The Existence of a Generalized Solution of an m-Point Nonlocal Boundary Value Problem

2017 ◽  
Vol 25 (2) ◽  
pp. 159-169 ◽  
Author(s):  
David Devadze
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Generalized Solution ◽  
Nonlocal Boundary Value Problem ◽  
Nonlocal Boundary Value Problems ◽  
First Order ◽  
Linear Differential ◽  
Generalized Analytic Function

Abstract An m-point nonlocal boundary value problem is posed for quasi- linear differential equations of first order on the plane. Nonlocal boundary value problems are investigated using the algorithm of reducing nonlocal boundary value problems to a sequence of Riemann-Hilbert problems for a generalized analytic function. The conditions for the existence and uniqueness of a generalized solution in the space are considered.

scholarly journals Nonlocal boundary value problem with Poissons operator on a rectangle and its difference interpretation

2020 ◽  
Vol 99 (3) ◽  
pp. 38-54
Author(s):  
D.M. Dovletov ◽  
◽  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Rectangular Domain ◽  
Nonlocal Boundary Value Problem ◽  
Weighted Integral ◽  
Accuracy Difference

In the present paper, differential and difference variants of nonlocal boundary value problem (NLBVP) for Poisson’s equation in open rectangular domain are studied. The existence, uniqueness and a priori estimate of classical solution are established. The second order of accuracy difference scheme is presented. The applications with weighted integral condition are provided in differential and difference variants.

scholarly journals New solvability condition of 2-d nonlocal boundary value problem for Poisson’s operator on rectangle

2021 ◽  
Vol 2021 (1) ◽  
pp. 12-28
Author(s):  
Dovlet M. Dovletov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
A Priori Estimate ◽  
Rectangular Domain ◽  
Nonlocal Boundary Value Problem ◽  
Order Of Accuracy ◽  
Solvability Conditions ◽  
Accuracy Difference

Abstract Differential and difference interpretations of a nonlocal boundary value problem for Poisson’s equation in open rectangular domain are studied. New solvability conditions are obtained in respect of existence, uniqueness and a priori estimate of the classical solution. Second order of accuracy difference scheme is presented.

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