A New Study on the Minimum Time of Null Controllability for the Fractional Heat Equation in One Dimension by the Action of a Strategic Zone Profile
The goal of this paper project is to find a minimum time null controllability of the fractional heat equation in one dimension using the notion of strategic zone actuators. As part of our research activities, we had already addressed this theme, and this publication project is a logical continuation...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/7279779 |
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| author | Cheikh Seck Mame Libasse Laye Ane Babacar Diouf |
| author_facet | Cheikh Seck Mame Libasse Laye Ane Babacar Diouf |
| author_sort | Cheikh Seck |
| collection | DOAJ |
| description | The goal of this paper project is to find a minimum time null controllability of the fractional heat equation in one dimension using the notion of strategic zone actuators. As part of our research activities, we had already addressed this theme, and this publication project is a logical continuation in the fractional case. Thus, this work has already been done in the case of classical differentiability in the sense of Frèchet. Indeed, inspired by the work of Khodja and Seck on the null controllability of the 1D heat equation and that of El Jai on the spreadability by means of the use of strategic actuators called zones, we have managed to decrease the minimum null controllability time of the 1D fractional heat equation. We are well aware of the difficulties linked to establishing the coercivity inequality of the parabolic operator. This requires searching for other, more innovative control methods. This is how, in this project, a mixed method using the method of moments and the notion of strategic profile was used to find a better minimum time of null controllability of the 1D fractional heat equation on regular domains by compared to what is known in the literature. |
| format | Article |
| id | doaj-art-245aba842d4a4aa79fc13677c0b21731 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-245aba842d4a4aa79fc13677c0b217312025-08-20T02:27:42ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/7279779A New Study on the Minimum Time of Null Controllability for the Fractional Heat Equation in One Dimension by the Action of a Strategic Zone ProfileCheikh Seck0Mame Libasse Laye Ane1Babacar Diouf2Laboratory of Digital Analysis and Computer Science (LANI) of the UFR SAT of the Gaston Berger University of Saint-LouisDepartment of Mathematics and Computer Science of the Faculty of Science and Technology of the Cheikh Anta Diop University of DakarDepartment of Mathematics and Computer Science of the Faculty of Science and Technology of the Cheikh Anta Diop University of DakarThe goal of this paper project is to find a minimum time null controllability of the fractional heat equation in one dimension using the notion of strategic zone actuators. As part of our research activities, we had already addressed this theme, and this publication project is a logical continuation in the fractional case. Thus, this work has already been done in the case of classical differentiability in the sense of Frèchet. Indeed, inspired by the work of Khodja and Seck on the null controllability of the 1D heat equation and that of El Jai on the spreadability by means of the use of strategic actuators called zones, we have managed to decrease the minimum null controllability time of the 1D fractional heat equation. We are well aware of the difficulties linked to establishing the coercivity inequality of the parabolic operator. This requires searching for other, more innovative control methods. This is how, in this project, a mixed method using the method of moments and the notion of strategic profile was used to find a better minimum time of null controllability of the 1D fractional heat equation on regular domains by compared to what is known in the literature.http://dx.doi.org/10.1155/2024/7279779 |
| spellingShingle | Cheikh Seck Mame Libasse Laye Ane Babacar Diouf A New Study on the Minimum Time of Null Controllability for the Fractional Heat Equation in One Dimension by the Action of a Strategic Zone Profile Journal of Mathematics |
| title | A New Study on the Minimum Time of Null Controllability for the Fractional Heat Equation in One Dimension by the Action of a Strategic Zone Profile |
| title_full | A New Study on the Minimum Time of Null Controllability for the Fractional Heat Equation in One Dimension by the Action of a Strategic Zone Profile |
| title_fullStr | A New Study on the Minimum Time of Null Controllability for the Fractional Heat Equation in One Dimension by the Action of a Strategic Zone Profile |
| title_full_unstemmed | A New Study on the Minimum Time of Null Controllability for the Fractional Heat Equation in One Dimension by the Action of a Strategic Zone Profile |
| title_short | A New Study on the Minimum Time of Null Controllability for the Fractional Heat Equation in One Dimension by the Action of a Strategic Zone Profile |
| title_sort | new study on the minimum time of null controllability for the fractional heat equation in one dimension by the action of a strategic zone profile |
| url | http://dx.doi.org/10.1155/2024/7279779 |
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