scholarly journals On an inverse boundary-value problem for a second-order elliptic equation with non-classical boundary conditions

2020 ◽  
Vol 41 (2) ◽  
pp. 443-455
Author(s):  
Prof.dr.rauf AMİROV ◽  
Yaşar MEHRALİYEV ◽  
Nergiz HEYDARZADE
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Second Order ◽  
Order Elliptic Equation ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem ◽  
Second Order Elliptic Equation ◽  
Classical Boundary

scholarly journals On an inverse boundary value problem for the second order elliptic equation with additional integral condition

2013 ◽  
Author(s):  
Я.Т. Мегралиев
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Integral Condition ◽  
Second Order ◽  
Order Elliptic Equation ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem ◽  
Second Order Elliptic Equation

В работе исследована одна обратная краевая задача для эллиптического уравнения второго порядка с дополнительным интегральным условием первого рода. Сначала исходная задача сводится к эквивалентной задаче, для которой доказывается теорема существования и единственности решения. Далее, пользуясь этими фактами, доказывается существование и единственность классического решения исходной задачи.

scholarly journals AN INVERSE BOUNDARY VALUE PROBLEM FOR A SECOND ORDER ELLIPTIC EQUATION IN A RECTANGLE

2014 ◽  
Vol 19 (2) ◽  
pp. 241-256 ◽  
Author(s):  
Yashar T. Mehraliyev ◽  
Fatma Kanca
Keyword(s):  
Inverse Problem ◽  
Elliptic Equation ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Order Elliptic Equation ◽  
Inverse Boundary ◽  
Numerical Tests ◽  
Second Order Elliptic Equation

In this paper, the inverse problem of finding a coefficient in a second order elliptic equation is investigated. The conditions for the existence and uniqueness of the classical solution of the problem under consideration are established. Numerical tests using the finite-difference scheme combined with an iteration method is presented and the sensitivity of this scheme with respect to noisy overdetermination data is illustrated.

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