The problem of finding the kernels in the system for integro-differential acoustic equations

We pose the direct and inverse problem of finding the acoustic wave velocity and pressure, diagonal memory matrix for a reduced canonical system of integro-differential acoustic equations. The problems are replaced by a closed system of Volterra-type integral equations of the second kind with respec...

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Bibliographic Details
Main Authors: Bozorov, Zavqiddin, Turdiev, Halim
Format: Conference Proceeding
Language:English
Subjects:
Acoustic waves
Continuity (mathematics)
Differential equations
Existence theorems
Fourier transforms
Integral equations
Inverse problems
Mathematical analysis
Uniqueness theorems
Wave velocity
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Summary:We pose the direct and inverse problem of finding the acoustic wave velocity and pressure, diagonal memory matrix for a reduced canonical system of integro-differential acoustic equations. The problems are replaced by a closed system of Volterra-type integral equations of the second kind with respect to the Fourier transform in the variables x1 and x2 of the solution of the unknowns of the direct problem and the inverse problem. To this system, we then apply a reduction method, a mapping in the space of continuous functions with a weighted norm. Thus, we prove global existence and uniqueness theorems to solve the given problems.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0199964