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Vol. 24, No. 4. P. 28–33

Adyghe Int. Sci. J. Vol. 24, No. 4. P. 28–33. 

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DOI: https://doi.org/10.47928/1726-9946-2024-24-4-28-33
EDN: LBSYJS

MATHEMATICS

MSC 35K10 Original Article

On a control problem

for the diffusion equation

Mikhail Sergeevich Ivshin
intern researcher of the Department of Mixed-type Equations Institute of Applied Mathematics and Automation KBSC RAS (360000, Kabardino-Balkarian Republic, Nalchik, 89A Shortanov St.), ORCID ID: https://orcid.org/0000-0002-0893-281X, mixail.ivshin.1996@mail.ru

Abstract. The paper presents the formulation and study of the optimal control problem for the diffusion equation. The peculiarity of this problem is that the control is the value of solving the diffusion equation at the initial moment of time.For controls that can be represented as polynomials in even degrees the existence and uniqueness of the solution of the problem are proved.

Keywords: diffusion equation, optimal control, polynomial, system of algebraic equations.

Funding. This work was carried out within the framework of the state assignment of the Ministry of Education and Science of the Russian Federation under the project: Boundary value and control problems for basic and mixed types of equations and their application to the study of systems with distributed parameters (1021032421196-2).
Competing interests. There are no conflicts of interest regarding authorship and publication.
Contribution and Responsibility. The author participated in the writing of the article and is fully responsible for submitting the final version of the article to the press.

For citation. Ivshin M. S. On a control problem for the diffusion equation. Adyghe Int. Sci. J. 2024. Vol. 24, No. 4. Pp. 28–33. DOI: https://doi.org/10.47928/1726-9946-2024-24-4-28-33; EDN: LBSYJS

Submitted 21.11.2024; approved after reviewing 18.12.2024; accepted for publication 19.12.2024.

© Ivshin M. S., 2024

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