scholarly journals On an Inverse Boundary Value Problem for a Fourth Order Elliptic Equation with Integral Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yashar T. Mehraliyev
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Initial Problem ◽  
Order Elliptic Equation ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem ◽  
Fourth Order Elliptic Equation

An inverse boundary value problem for a fourth order elliptic equation is investigated. At first the initial problem is reduced to the equivalent problem for which the existence and uniqueness theorem of the solution is proved. Further, using these facts, the existence and uniqueness of the classic solution of the initial problem are proved.

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 Nonlocal inverse boundary-value problem for a 2D parabolic equation with integral overdetermination condition

2020 ◽  
Vol 12 (1) ◽  
pp. 23-33
Author(s):  
E.I. Azizbayov ◽  
Y.T. Mehraliyev
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Original Problem ◽  
Boundary Value ◽  
Auxiliary Problem ◽  
Rectangular Domain ◽  
Unknown Coefficient ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem

This article studies a nonlocal inverse boundary-value problem for a two-dimensional second-order parabolic equation in a rectangular domain. The purpose of the article is to determine the unknown coefficient and the solution of the considered problem. To investigate the solvability of the inverse problem, we transform the original problem into some auxiliary problem with trivial boundary conditions. Using the contraction mappings principle, existence and uniqueness of the solution of an equivalent problem are proved. Further, using the equivalency, the existence and uniqueness theorem of the classical solution of the original problem is obtained.

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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