THE UNIQUE SOLVABILITY OF A NONLOCAL INVERSE BOUNDARY-VALUE PROBLEM FOR THE PSEUDO-HYPERBOLIC EQUATION OF FOURTH ORDER

2021 ◽  
Vol 24 (1) ◽  
pp. 79-100
Author(s):  
Elvin I. Azizbayov
Keyword(s):  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Fourth Order ◽  
Unique Solvability ◽  
Boundary Value ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem

scholarly journals Recovery of unknown coefficients in a two-dimensional hyperbolic equation with additional conditions

2021 ◽  
Author(s):  
Elvin Azizbayov ◽  
He Yang ◽  
Yashar Mehraliyev
Keyword(s):  
Inverse Problem ◽  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Original Problem ◽  
Boundary Value ◽  
Auxiliary Problem ◽  
Fourier Method ◽  
Two Dimensional ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem

In this paper, a nonlocal inverse boundary value problem for a two-dimensional hyperbolic equation with overdetermination conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary value problem and prove its equivalence (in a certain sense) to the original problem. Then using the Fourier method, solving an equivalent problem is reduced to solving a system of integral equations and by the contraction mappings principle the existence and uniqueness theorem for auxiliary problem is proved. Further, on the basis of the equivalency of these problems the uniquely existence theorem for the classical solution of the considered inverse problem is proved and some considerations on the numerical solution for this inverse problem are presented with the examples.

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.

A probe method for the inverse boundary value problem of non-stationary heat equations

2007 ◽  
Vol 23 (5) ◽  
pp. 1787-1800 ◽  
Author(s):  
Yuki Daido ◽  
Hyeonbae Kang ◽  
Gen Nakamura
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Probe Method ◽  
Heat Equations ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem ◽  
Stationary Heat
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