The null boundary controllability for the Mullins equation with periodic boundary conditions
In this paper, we study the null controllability of the Mullins equation with the control acting on the periodic boundary. Firstly, using the duality relation between controllability and observability, we express the controllability condition in terms of the solution of the backward adjoint system....
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| Format: | Article |
| Language: | English |
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Balikesir University
2023-01-01
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| Series: | An International Journal of Optimization and Control: Theories & Applications |
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| Online Access: | http://ijocta.org/index.php/files/article/view/1283 |
| _version_ | 1797909023036538880 |
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| author | Isil Oner |
| author_facet | Isil Oner |
| author_sort | Isil Oner |
| collection | DOAJ |
| description |
In this paper, we study the null controllability of the Mullins equation with the control acting on the periodic boundary. Firstly, using the duality relation between controllability and observability, we express the controllability condition in terms of the solution of the backward adjoint system. After showing the existence and uniqueness of the solution of the adjoint system, we determine the admissible initial data class since the system is not always controllable under these boundary conditions. Finally, using this spectral analysis, we reduce the null controllability problem to the moment problem and solve the problem on this admissible initial class.
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| first_indexed | 2024-04-10T11:03:02Z |
| format | Article |
| id | doaj.art-58a1fd2512c24328b8bef16e889bf610 |
| institution | Directory Open Access Journal |
| issn | 2146-0957 2146-5703 |
| language | English |
| last_indexed | 2024-04-10T11:03:02Z |
| publishDate | 2023-01-01 |
| publisher | Balikesir University |
| record_format | Article |
| series | An International Journal of Optimization and Control: Theories & Applications |
| spelling | doaj.art-58a1fd2512c24328b8bef16e889bf6102023-02-15T16:19:35ZengBalikesir UniversityAn International Journal of Optimization and Control: Theories & Applications2146-09572146-57032023-01-0113110.11121/ijocta.2023.1283The null boundary controllability for the Mullins equation with periodic boundary conditionsIsil Oner0Department of Mathematics in Faculty of Science, Gebze Technical University, Turkey In this paper, we study the null controllability of the Mullins equation with the control acting on the periodic boundary. Firstly, using the duality relation between controllability and observability, we express the controllability condition in terms of the solution of the backward adjoint system. After showing the existence and uniqueness of the solution of the adjoint system, we determine the admissible initial data class since the system is not always controllable under these boundary conditions. Finally, using this spectral analysis, we reduce the null controllability problem to the moment problem and solve the problem on this admissible initial class. http://ijocta.org/index.php/files/article/view/1283Null controllabilityMullins equationmoment methodperiodic boundary condiitionOne-dimensional fourth order parabolic equations. |
| spellingShingle | Isil Oner The null boundary controllability for the Mullins equation with periodic boundary conditions An International Journal of Optimization and Control: Theories & Applications Null controllability Mullins equation moment method periodic boundary condiition One-dimensional fourth order parabolic equations. |
| title | The null boundary controllability for the Mullins equation with periodic boundary conditions |
| title_full | The null boundary controllability for the Mullins equation with periodic boundary conditions |
| title_fullStr | The null boundary controllability for the Mullins equation with periodic boundary conditions |
| title_full_unstemmed | The null boundary controllability for the Mullins equation with periodic boundary conditions |
| title_short | The null boundary controllability for the Mullins equation with periodic boundary conditions |
| title_sort | null boundary controllability for the mullins equation with periodic boundary conditions |
| topic | Null controllability Mullins equation moment method periodic boundary condiition One-dimensional fourth order parabolic equations. |
| url | http://ijocta.org/index.php/files/article/view/1283 |
| work_keys_str_mv | AT isiloner thenullboundarycontrollabilityforthemullinsequationwithperiodicboundaryconditions AT isiloner nullboundarycontrollabilityforthemullinsequationwithperiodicboundaryconditions |