# Vestnik KRAUNC. Fiz.-Mat. nauki. 2022. vol. 39. no. 2. P. 32-41. ISSN 2079-6641

**MSC 35J15 **

**Research Article**

**On one boundary value problem for the fourth-order equation in partial derivatives**

**O. Sh. Kilichov¹, A. N. Ubaydullaev²**

¹V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 4b University str., Tashkent, 100174, Uzbekistan

²Bukhara State University, M. Ikbol str. 11, Bukhara, 705018, Uzbekistan

E-mail: oybek2402@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: boundary value problem; Fourier method; the existence of a solution; the uniqueness of a solution.*

**DOI: 10.26117/2079-6641-2022-39-2-32-41**

**Original article submitted: 17.07.2022 **

**Revision submitted: 10.08.2022**

**For citation.** Kilichov O. Sh., Ubaydullaev A. N. On one boundary value problem for the fourth-order equation in partial derivatives. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 39: 2, 32-41. DOI: 10.26117/2079-6641-2022-39-2-32-41

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)

© Kilichov O. Sh., Ubaydullaev A. N., 2022

**Competing interests.** The authors declare that there are no conflicts of interest regarding authorship and publication.

**Contribution and Responsibility.** All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

**Acknowledgments.** The authors are deeply grateful to the referee for a number of comments that contributed to the improvement of the article.

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* Kilichov Oybek Sharafiddinovich* – Doctoral student, Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan, ORCID 0000-0002-7673-943X.

* Ubaydullaev Alisher Nematillayevich* – Teacher of the Department of Mathematics of Bukhara State University, Bukhara, Uzbekistan, ORCID 0000-0002-4219-5155.