scholarly journals Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials

2015 ◽  
Vol 9 (3) ◽  
pp. 709-723 ◽  
Author(s):  
Masahiro Yamamoto ◽  
Oleg Imanuvilov ◽  
Eemeli Blåsten
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Two Dimensional ◽  
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.

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