Uniqueness of a Solution to the Lavrent’ev Integral Equation in n-Dimensional Space

We study the multidimensional analogue of the Lavrent’ev integral equation to which an inverse problem of acoustic sounding is reduced. Conditions under which the studied equation has a unique solution are established. Results of numerical experiments concerning the solution of the inverse acoustic...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 64; no. 3; pp. 416 - 431
Main Authors: Kokurin, M. M., Klyuchev, V. V., Gavrilova, A. V.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.03.2024
Springer Nature B.V
Subjects:
Acoustic sounding
Acoustics
Computational Mathematics and Numerical Analysis
Integral equations
Inverse problems
Laplace transforms
Mathematics
Mathematics and Statistics
Partial Differential Equations
coefficient inverse problem
solution uniqueness
linear integral equation
Lavrent’ev equation
complete system of functions
uniqueness set
inverse problem of acoustics
hyperbolic equation
harmonic functions
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary:We study the multidimensional analogue of the Lavrent’ev integral equation to which an inverse problem of acoustic sounding is reduced. Conditions under which the studied equation has a unique solution are established. Results of numerical experiments concerning the solution of the inverse acoustic problem with variously located sets of sources and detectors are presented.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542524030084