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Optimal Control by a Discrete Heat Flux for a Homogeneous Half-Line Научная публикация

Журнал

Numerical Analysis and Applications
ISSN: 1995-4239

Вых. Данные

Год: 2026, Том: 19, Номер: 2, Страницы: 113-121 Страниц : 9 DOI: 10.1134/s1995423926020047

Ключевые слова

optimal heating control, heat equation, semi-infinite line, solution with bounded upper value

Авторы

Markov B.A. ¹ , Sidikova A.I. ² , Gainova I.A. ³

Организации

1	School of Electronic Engineering and Computer Science, South Ural State University, Chelyabinsk, Russian Federation
2	Institute of Natural Sciences and Mathematics, South Ural State University, Chelyabinsk, Russian Federation
3	Sobolev Institute of Mathematics SB RAS, Prosp. Akad. Koptyuga, Novosibirsk, Russian Federation

Информация о финансировании (1)

Министерство науки и высшего образования РФ

FWNF-2026-0005

The article studies a problem of optimal control of heating for a homogeneous halfline. The heating problem is set for a heat conduction equation defined on a half-line where the temperature tends to zero at infinity. At the origin of the spatial coordinate a heat flux, i. e. a nonhomogeneous boundary condition of the second kind, is given. The heat flux is modeled using a heating function which is a continuous broken line. This choice of the function is explained by the properties of the technical device under study. Furthermore, it it proved that there exists a solution to such a problem and that its classical solution within a certain error is unique. Also the optimality of the heating control in our reasoning means that at the boundary x = 0 the temperature at any time is maximum permissible (or, in the first time interval, maximum possible) and, at the same time, does not exceed a certain critical value, which is chosen to be equal to 1. For the optimal control, a recurrence formula is found at different times, and it is shown that this is exactly the optimal solution. In other words, at larger values of the heat flux the critical temperature at the boundary will be exceeded at some point in time, and at smaller values the temperature will be lower than that allowed by the material. Finally, it is stated that the heat flux found is the exact upper bound of all admissible heat fluxes for a given discrete control and that such a flux is unique.

Markov B.A. , Sidikova A.I. , Gainova I.A.
Optimal Control by a Discrete Heat Flux for a Homogeneous Half-Line
Numerical Analysis and Applications. 2026. V.19. N2. P.113-121. DOI: 10.1134/s1995423926020047 Scopus OpenAlex

Марков Б.А. , Сидикова А.И. , Гайнова И.А.
Оптимальное управление дискретным потоком тепла на однородной полупрямой
Сибирский журнал вычислительной математики. 2026. Т.29. №2. С.145-154. DOI: 10.15372/SJNM20260204 РИНЦ OpenAlex

Поступила в редакцию:	4 апр. 2025 г.
Принята к публикации:	15 янв. 2026 г.
Опубликована в печати:	29 июл. 2026 г.
Опубликована online:	29 июл. 2026 г.

≡ Scopus:	2-s2.0-105046198012
≡ OpenAlex:	W7171640362