SOLVABILITY OF THE INVERSE PROBLEM FOR THE PSEUDOHYPERBOLIC EQUATION
This paper investigates the solvability of the inverse problem of finding a solution and an unknown coefficient in a pseudohyperbolic equation known as the Klein-Gordon equation. A distinctive feature of the given problem is that the unknown coefficient is a function that depends only on the time va...
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| Format: | Article |
| Language: | English |
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Al-Farabi Kazakh National University
2022-09-01
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| Series: | Вестник КазНУ. Серия математика, механика, информатика |
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| Online Access: | https://bm.kaznu.kz/index.php/kaznu/article/view/1164/677 |
| _version_ | 1811173471838797824 |
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| author | S. Aitzhanov J. Ferreira K. Zhalgassova |
| author_facet | S. Aitzhanov J. Ferreira K. Zhalgassova |
| author_sort | S. Aitzhanov |
| collection | DOAJ |
| description | This paper investigates the solvability of the inverse problem of finding a solution and an unknown coefficient in a pseudohyperbolic equation known as the Klein-Gordon equation. A distinctive feature of the given problem is that the unknown coefficient is a function that depends only on the time variable. The problem is considered in the cylinder, the conditions of the usual initial-boundary value problem are set. The integral overdetermination condition is used as an additional condition. In this paper, the inverse problem is reduced to an equivalent problem for the loaded nonlinear pseudohyperbolic equation. Such equations belong to the class of partial differential equations, not resolved with respect to the highest time derivative, and they are also called composite type equations. The proof uses the Galerkin method and the compactness method (using the obtained a priori estimates). For the problem under study, the authors prove existence and uniqueness theorems for the solution in appropriate classes. |
| first_indexed | 2024-04-10T17:48:36Z |
| format | Article |
| id | doaj.art-5c58978224e14c318e7c14171505b3b9 |
| institution | Directory Open Access Journal |
| issn | 1563-0277 2617-4871 |
| language | English |
| last_indexed | 2024-04-10T17:48:36Z |
| publishDate | 2022-09-01 |
| publisher | Al-Farabi Kazakh National University |
| record_format | Article |
| series | Вестник КазНУ. Серия математика, механика, информатика |
| spelling | doaj.art-5c58978224e14c318e7c14171505b3b92023-02-03T03:58:39ZengAl-Farabi Kazakh National UniversityВестник КазНУ. Серия математика, механика, информатика1563-02772617-48712022-09-011153315https://doi.org/10.26577/JMMCS.2022.v115.i3.01 SOLVABILITY OF THE INVERSE PROBLEM FOR THE PSEUDOHYPERBOLIC EQUATIONS. Aitzhanov0J. Ferreira1K. Zhalgassova2Al-Farabi Kazakh National University, Almaty, KazakhstanFederal University of FluminenseM.Auezov South Kazakhstan University, Kazakhstan, ShymkentThis paper investigates the solvability of the inverse problem of finding a solution and an unknown coefficient in a pseudohyperbolic equation known as the Klein-Gordon equation. A distinctive feature of the given problem is that the unknown coefficient is a function that depends only on the time variable. The problem is considered in the cylinder, the conditions of the usual initial-boundary value problem are set. The integral overdetermination condition is used as an additional condition. In this paper, the inverse problem is reduced to an equivalent problem for the loaded nonlinear pseudohyperbolic equation. Such equations belong to the class of partial differential equations, not resolved with respect to the highest time derivative, and they are also called composite type equations. The proof uses the Galerkin method and the compactness method (using the obtained a priori estimates). For the problem under study, the authors prove existence and uniqueness theorems for the solution in appropriate classes.https://bm.kaznu.kz/index.php/kaznu/article/view/1164/677pseudohyperbolic equationnverse problemklein-gordon equationgalerkin methodcompactness methodexistenceuniqueness |
| spellingShingle | S. Aitzhanov J. Ferreira K. Zhalgassova SOLVABILITY OF THE INVERSE PROBLEM FOR THE PSEUDOHYPERBOLIC EQUATION Вестник КазНУ. Серия математика, механика, информатика pseudohyperbolic equation nverse problem klein-gordon equation galerkin method compactness method existence uniqueness |
| title | SOLVABILITY OF THE INVERSE PROBLEM FOR THE PSEUDOHYPERBOLIC EQUATION |
| title_full | SOLVABILITY OF THE INVERSE PROBLEM FOR THE PSEUDOHYPERBOLIC EQUATION |
| title_fullStr | SOLVABILITY OF THE INVERSE PROBLEM FOR THE PSEUDOHYPERBOLIC EQUATION |
| title_full_unstemmed | SOLVABILITY OF THE INVERSE PROBLEM FOR THE PSEUDOHYPERBOLIC EQUATION |
| title_short | SOLVABILITY OF THE INVERSE PROBLEM FOR THE PSEUDOHYPERBOLIC EQUATION |
| title_sort | solvability of the inverse problem for the pseudohyperbolic equation |
| topic | pseudohyperbolic equation nverse problem klein-gordon equation galerkin method compactness method existence uniqueness |
| url | https://bm.kaznu.kz/index.php/kaznu/article/view/1164/677 |
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