# Vestnik КRAUNC. Fiz.-Mat. nauki. 2022. vol. 39. no. 2. P. 20-31. ISSN 2079-6641

**MSC 35K05, 35K15 **

**Research Article**

**On the control problem associated with the heating process in the bounded domain**

**F. N. Dekhkonov¹²**

¹National University of Uzbekistan named after Mirzo Ulugbek, 100174, University str., 4b, Tashkent, Uzbekistan

²Institute of Mathematics named after V. I. Romanovskiy, Academy of Sciences of the Republic of Uzbekistan, 100174, University str., 4b, Tashkent, Uzbekistan

E-mail: f.n.dehqonov@mail.ru

The initial-boundary problem for the heat conduction equation inside a bounded domain is considered. It is supposed that on the boundary of this domain the heat exchange takes place according to Newton’s law. The control parameter is equal to the magnitude of output of hot air and is defined on a givenmpart of the boundary. Then we determined the dependence T(θ) on the parameters of the temperature process when θ is close to critical value.

*Key words: heat conduction equation, admissible control, initial-boundary value problem, integral equation.*

**DOI: 10.26117/2079-6641-2022-39-2-20-31**

**Original article submitted: 01.07.2022 **

**Revision submitted: 10.08.2022**

**For citation.** Dekhkonov F. N. On the control problem associated with the heating process in the bounded domain. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 39: 2, 20-31. DOI: 10.26117/2079-6641-2022-39-2-20-31

The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)

© Dekhkonov F. N., 2022

**Competing interests.** The author declares no conflicts of interest with respect to authorship and publication.

**Contribution and responsibility.** The author has contributed to this article. The author is solely responsible for providing the final version of the article for publication.

**Acknowledgements.** The author is grateful to Academician Sh. A. Alimov for his valuable comments.

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* Dekhkonov Farrukh Nuriddin ugli *– Ph.D. (Phys. & Math.), National University of Uzbekistan named after M.Ulugbek, Tashkent, Uzbekistan, ORCID 0000-0003-4747-8557.