Uniqueness of the solution of the Gellerstedt problem for an equation of mixed type

1978 ◽  
Vol 18 (6) ◽  
pp. 1010-1013
Author(s):  
Khe Kan Cher
Keyword(s):  
Mixed Type ◽  
Gellerstedt Problem ◽  
Uniqueness Of The Solution ◽  
Equation Of Mixed Type

A boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in the boundary conditions

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Oleg A. Repin ◽  
Svetlana K. Kumykova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Mixed Type ◽  
Original Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Fractional Differentiation ◽  
Uniqueness Of Solutions ◽  
Uniqueness Of The Solution ◽  
Equation Of Mixed Type

AbstractThe paper is devoted to the study of a boundary-value problem for an equation of mixed type with generalized operators of fractional differentiation in boundary conditions. We prove uniqueness of solutions under some restrictions on the known functions and on the different orders of the operators of generalized fractional differentiation appearing in the boundary conditions. Existence of solutions is proved by reduction to a Fredholm equation of the second kind, for which solvability follows from the uniqueness of the solution of our original problem.

scholarly journals A BOUNDARY VALUE PROBLEM WITH AN OFFSET FOR A MODEL EQUATION OF MIXED TYPE IN AN UNBOUNDED DOMAIN

2020 ◽  
pp. 31-41
Author(s):  
Р.Т. Зуннунов ◽  
Ж.А. Толибжонов
Keyword(s):  
Mixed Type ◽  
Model Equation ◽  
Type Equation ◽  
Green Functions ◽  
Horizontal Strip ◽  
Existence Of A Solution ◽  
Method Of Integral Equations ◽  
Energy Integrals ◽  
Uniqueness Of The Solution ◽  
Equation Of Mixed Type

В данной работе для уравнения смешанного типа в неограниченной области эллиптическая часть которой является горизонтальной полосой исследуется задача со смещением на характеристиках разных семейств. Единственность решения задачи доказывается методом интегралов энергии, а существование решения задачи методом функций Грина и методом интегральных уравнений. In this paper, for a mixed type equation in an unbounded region, the elliptical part of which is a horizontal strip, we study the problem with a shift on the characteristics of different families. The uniqueness of the solution of the problem is proved by the method of energy integrals, and the existence of a solution of the problem by the method of Green functions and the method of integral equations.

Sign in / Sign up

Export Citation Format

Share Document