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.

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 On the Existence and Uniqueness ofRv-Generalized Solution for Dirichlet Problem with Singularity on All Boundary

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
V. Rukavishnikov ◽  
E. Rukavishnikova
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Input Data ◽  
Generalized Solution ◽  
Two Dimensional ◽  
Order Elliptic Equation ◽  
Second Order Elliptic Equation ◽  
Dimensional Domain

The existence and uniqueness of theRv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.

The Dirichlet Problem for a Second Order Elliptic Equation Degenerating on the Whole Boundary When the Boundary Condition Is Satisfied in the Presence of Some Weight

2006 ◽  
Vol 13 (3) ◽  
pp. 573-579
Author(s):  
Mikheil Usanetashvili
Keyword(s):  
Boundary Condition ◽  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Boundary Value Problem ◽  
General Type ◽  
Type Equation ◽  
Second Order ◽  
Elliptic Type ◽  
Order Elliptic Equation ◽  
Second Order Elliptic Equation

Abstract The first boundary value problem with weight is investigated for a general-type second order elliptic type equation degenerating on the whole boundary.

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