On the time-optimal control problem for a heat equation
In previous works, we have considered some control problems for parabolic type equations, namely, control problems for parabolic type equations were studied as boundary value problems of the first type, and the weight function was expanded into a Fourier series by sines. In this paper, we consider...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2023-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/580 |
| _version_ | 1797372759255285760 |
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| author | F.N. Dekhkonov |
| author_facet | F.N. Dekhkonov |
| author_sort | F.N. Dekhkonov |
| collection | DOAJ |
| description |
In previous works, we have considered some control problems for parabolic type equations, namely, control problems for parabolic type equations were studied as boundary value problems of the first type, and the weight function was expanded into a Fourier series by sines. In this paper, we consider boundary control problem for a heat equation on the interval. In the part of the bound of the given domain it is given value of a solution and it is required to find a control to get the average value of the solution. By the mathematical-physics methods it is proved that like this control exists and the estimate of a minimal time for achieving the given average temperature over some domain is found.
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| first_indexed | 2024-03-08T18:39:29Z |
| format | Article |
| id | doaj.art-f738aab3c4314516894cb49f4bb60cd1 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:39:29Z |
| publishDate | 2023-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-f738aab3c4314516894cb49f4bb60cd12023-12-29T10:18:51ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112023-09-01111310.31489/2023m3/28-38On the time-optimal control problem for a heat equationF.N. Dekhkonov In previous works, we have considered some control problems for parabolic type equations, namely, control problems for parabolic type equations were studied as boundary value problems of the first type, and the weight function was expanded into a Fourier series by sines. In this paper, we consider boundary control problem for a heat equation on the interval. In the part of the bound of the given domain it is given value of a solution and it is required to find a control to get the average value of the solution. By the mathematical-physics methods it is proved that like this control exists and the estimate of a minimal time for achieving the given average temperature over some domain is found. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/580heat equationminimal timeadmissible controlintegral equationinitial-boundary value problem |
| spellingShingle | F.N. Dekhkonov On the time-optimal control problem for a heat equation Қарағанды университетінің хабаршысы. Математика сериясы heat equation minimal time admissible control integral equation initial-boundary value problem |
| title | On the time-optimal control problem for a heat equation |
| title_full | On the time-optimal control problem for a heat equation |
| title_fullStr | On the time-optimal control problem for a heat equation |
| title_full_unstemmed | On the time-optimal control problem for a heat equation |
| title_short | On the time-optimal control problem for a heat equation |
| title_sort | on the time optimal control problem for a heat equation |
| topic | heat equation minimal time admissible control integral equation initial-boundary value problem |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/580 |
| work_keys_str_mv | AT fndekhkonov onthetimeoptimalcontrolproblemforaheatequation |