A time-nonlocal inverse problem for a hyperbolic equation with an integral overdetermination condition
This article is concerned with the study of the unique solvability of a time-nonlocal inverse boundary value problem for second-order hyperbolic equation with an integral overdetermination condition. To study the solvability of the inverse problem, we first reduce the considered problem to an auxili...
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| Format: | Article |
| Language: | English |
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University of Szeged
2021-04-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8993 |
| _version_ | 1797830423404871680 |
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| author | Yashar Mehraliyev Elvin Azizbayov |
| author_facet | Yashar Mehraliyev Elvin Azizbayov |
| author_sort | Yashar Mehraliyev |
| collection | DOAJ |
| description | This article is concerned with the study of the unique solvability of a time-nonlocal inverse boundary value problem for second-order hyperbolic equation with an integral overdetermination condition. To study the solvability of the inverse problem, we first reduce the considered problem to an auxiliary system with trivial data and prove its equivalence (in a certain sense) to the original problem. Then using the Banach fixed point principle, the existence and uniqueness of a solution to this system is shown. Further, on the basis of the equivalency of these problems the existence and uniqueness theorem for the classical solution of the inverse coefficient problem is proved for the smaller value of time. |
| first_indexed | 2024-04-09T13:36:59Z |
| format | Article |
| id | doaj.art-259aaa6c6a354aeca79618c252587f75 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:59Z |
| publishDate | 2021-04-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-259aaa6c6a354aeca79618c252587f752023-05-09T07:53:11ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752021-04-0120212811210.14232/ejqtde.2021.1.288993A time-nonlocal inverse problem for a hyperbolic equation with an integral overdetermination conditionYashar Mehraliyev0Elvin Azizbayov1Department of Differential Equations, Baku State University, Baku, Azerbaijan The Academy of Public Administration under the President of the Republic of Azerbaijan, Baku, AzerbaijanThis article is concerned with the study of the unique solvability of a time-nonlocal inverse boundary value problem for second-order hyperbolic equation with an integral overdetermination condition. To study the solvability of the inverse problem, we first reduce the considered problem to an auxiliary system with trivial data and prove its equivalence (in a certain sense) to the original problem. Then using the Banach fixed point principle, the existence and uniqueness of a solution to this system is shown. Further, on the basis of the equivalency of these problems the existence and uniqueness theorem for the classical solution of the inverse coefficient problem is proved for the smaller value of time.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8993inverse problemhyperbolic equationoverdetermination conditionclassical solutionexistenceuniqueness |
| spellingShingle | Yashar Mehraliyev Elvin Azizbayov A time-nonlocal inverse problem for a hyperbolic equation with an integral overdetermination condition Electronic Journal of Qualitative Theory of Differential Equations inverse problem hyperbolic equation overdetermination condition classical solution existence uniqueness |
| title | A time-nonlocal inverse problem for a hyperbolic equation with an integral overdetermination condition |
| title_full | A time-nonlocal inverse problem for a hyperbolic equation with an integral overdetermination condition |
| title_fullStr | A time-nonlocal inverse problem for a hyperbolic equation with an integral overdetermination condition |
| title_full_unstemmed | A time-nonlocal inverse problem for a hyperbolic equation with an integral overdetermination condition |
| title_short | A time-nonlocal inverse problem for a hyperbolic equation with an integral overdetermination condition |
| title_sort | time nonlocal inverse problem for a hyperbolic equation with an integral overdetermination condition |
| topic | inverse problem hyperbolic equation overdetermination condition classical solution existence uniqueness |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8993 |
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