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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| Vydáno v: | Computational mathematics and mathematical physics Ročník 64; číslo 3; s. 416 - 431 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Moscow
Pleiades Publishing
01.03.2024
Springer Nature B.V |
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| ISSN: | 0965-5425, 1555-6662 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Kokurin, M. M. Gavrilova, A. V. Klyuchev, V. V. |
| Author_xml | – sequence: 1 givenname: M. M. surname: Kokurin fullname: Kokurin, M. M. email: kokurin@nextmail.ru organization: Mari State University – sequence: 2 givenname: V. V. surname: Klyuchev fullname: Klyuchev, V. V. organization: Mari State University – sequence: 3 givenname: A. V. surname: Gavrilova fullname: Gavrilova, A. V. organization: Mari State University |
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| Cites_doi | 10.1137/20M1376558 10.1134/S0001434618110093 10.1134/S0965542521090128 10.1023/B:SIMJ.0000035828.43530.0c 10.1134/S0965542520060032 10.1007/s10958-023-06613-9 10.1134/S0965542508010089 10.1515/jip-2012-0082 10.1134/S0012266121020129 10.3103/S1066369X20060055 10.1007/s11202-009-0080-x 10.4213/im9253e |
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| Copyright | Pleiades Publishing, Ltd. 2024. ISSN 0965-5425, Computational Mathematics and Mathematical Physics, 2024, Vol. 64, No. 3, pp. 416–431. © Pleiades Publishing, Ltd., 2024. Pleiades Publishing, Ltd. 2024. |
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| Keywords | 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 |
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| SubjectTerms | Acoustic sounding Acoustics Computational Mathematics and Numerical Analysis Integral equations Inverse problems Laplace transforms Mathematics Mathematics and Statistics Partial Differential Equations |
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| Title | Uniqueness of a Solution to the Lavrent’ev Integral Equation in n-Dimensional Space |
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