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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 44

Solution of the Inverse Problem Describing Slow Thermal Convection in a Rotating Layer

Author(s)
Viktor K. Andreev1, Liliya I. Latonova2

1Institute of Computational Modeling SB RAS, Krasnoyarsk, Russian Federation

2Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract
The linear inverse initial-boundary value problem arising when modeling the rotational motion of a viscous heat-conducting liquid in a flat layer is solved. It is shown that the problem has two different integral identities. Based on these identities, a priori estimates of the solution in a uniform metric are obtained and its uniqueness is proved. The conditions for the input data are also determined, under which this solution goes to the stationary mode with increasing time according to the exponential law. In the final part, the existence of a unique classical solution of the inverse problem is proved. To do this, differentiating the problem by a spatial variable, we come to a direct non-classical problem with two integral conditions instead of the usual boundary conditions. The new problem is solved by the method of separation of variables, which makes it possible to find a solution in the form of rapidly converging series on a special basis.
About the Authors

Victor K. Andreev, Dr. Sci. (Phys.–Math.), Prof., Department of Differential Equations of Mechanics, Institute of Computational Modeling SB RAS, Krasnoyarsk, 660036, Russian Federation, andr@icm.krasn.ru

Liliya I. Latonova, Postgraduate, Siberian Federal University, Krasnoyarsk, 660041, Russian Federation, liliyalatonova@gmail.com

For citation
Andreev V. K., Latonova L. I. Solution of the inverse problem describing slow thermal convection in a rotating layer. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 44, pp. 3–18. (in Russian) https://doi.org/10.26516/1997-7670.2023.44.3
Keywords
thermal convection, liquid motion, inverse problem, stationary solution
UDC
517.956: 532.5.032
MSC
31B20, 76D05
DOI
https://doi.org/10.26516/1997-7670.2023.44.3
References
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